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Celebratio Mathematica

Lou van den Dries

Complete Works

[1] L. van den Dries: “Artin–Schreier the­ory for com­mut­at­ive reg­u­lar rings,” Ann. Math. Lo­gic 12 : 2 (December 1977), pp. 113–​150. MR 498094 Zbl 0376.​13012 article

[2] L. P. D. van den Dries: Mod­el the­ory of fields: De­cid­ab­il­ity, and bounds for poly­no­mi­al ideals. Ph.D. thesis, Utrecht Uni­versity, 1978. Ad­vised by D. van Dalen. phdthesis

[3] L. P. D. van den Dries: Mod­el the­ory of fields: De­cid­ab­il­ity and bounds for poly­no­mi­al ideals. Ph.D. thesis, Rijk­suni­versiteit Utrecht, 1978. phdthesis

[4] J. Beck­er, J. Denef, L. Lip­shitz, and L. van den Dries: “Ul­traproducts and ap­prox­im­a­tion in loc­al rings, I,” In­vent. Math. 51 : 2 (June 1979), pp. 189–​203. MR 528023 Zbl 0416.​13004 article

[5] L. van den Dries and P. Riben­boim: “Ap­plic­a­tion de la théorie des modèles aux groupes de Galois de corps de fonc­tions” [Ap­plic­a­tion of mod­el the­ory to Galois groups of func­tion fields], C. R. Acad. Sci. Par­is Sér. A-B 288 : 17 (1979), pp. A789–​A792. MR 535636 Zbl 0426.​12004 article

[6] L. van den Dries: “New de­cid­able fields of al­geb­ra­ic num­bers,” Proc. Am. Math. Soc. 77 : 2 (November 1979), pp. 251–​256. MR 542093 Zbl 0396.​12020 article

[7] L. van den Dries: “Al­gorithms and bounds for poly­no­mi­al rings,” pp. 147–​157 in Lo­gic col­loqui­um ’78 (Mons, Bel­gi­um, 24 Au­gust–1 Septem­ber 1978). Edi­ted by M. Boffa, D. Dalen, and K. Mc­A­loon. Stud­ies in Lo­gic and the Found­a­tions of Math­em­at­ics 97. North-Hol­land (Am­s­ter­dam and New York), 1979. MR 567669 Zbl 0461.​13015 incollection

[8] L. P. D. van den Dries: “A lin­early ordered ring whose the­ory ad­mits elim­in­a­tion of quan­ti­fi­ers is a real closed field,” Proc. Am. Math. Soc. 79 : 1 (May 1980), pp. 97–​100. MR 560592 Zbl 0397.​06017 article

[9] L. van den Dries: “Some mod­el the­ory and num­ber the­ory for mod­els of weak sys­tems of arith­met­ic,” pp. 346–​362 in Mod­el the­ory of al­gebra and arith­met­ic (Karpacz, Po­land, 1–7 Septem­ber 1979). Edi­ted by L. Pachol­ski, J. Wi­erze­jew­ski, and A. J. Wilkie. Lec­ture Notes in Math­em­at­ics 834. Spring­er, 1980. MR 606793 Zbl 0454.​03034 incollection

[10] G. Cher­lin, L. van den Dries, and A. Macintyre: “De­cid­ab­il­ity and un­de­cid­ab­il­ity the­or­ems for PAC-fields,” Bull. Am. Math. Soc. (N.S.) 4 : 1 (1981), pp. 101–​104. MR 590820 Zbl 0466.​12017 article

[11] L. van den Dries: “Which curves over \( \mathbf{Z} \) have points with co­ordin­ates in a dis­crete ordered ring?,” Trans. Am. Math. Soc. 264 : 1 (March 1981), pp. 181–​189. MR 597875 Zbl 0464.​10047 article

[12] A. Lub­otzky and L. van den Dries: “Sub­groups of free profin­ite groups and large sub­fields of \( \tilde{\mathbf{Q}} \),” Is­rael J. Math. 39 : 1–​2 (March 1981), pp. 25–​45. MR 617288 Zbl 0485.​20021 article

[13] L. van den Dries: “Quan­ti­fi­er elim­in­a­tion for lin­ear for­mu­las over ordered and val­ued fields,” Bull. Soc. Math. Belg. Sér. B 33 : 1 (1981), pp. 19–​31. MR 620959 Zbl 0479.​03018 article

[14] L. van den Dries: “A spe­cial­iz­a­tion the­or­em for \( p \)-ad­ic power series con­ver­ging on the closed unit disc,” J. Al­gebra 73 : 2 (December 1981), pp. 613–​623. MR 640053 Zbl 0511.​12018 article

[15] L. P. D. van den Dries, A. M. W. Glass, A. Macintyre, A. H. Mekler, and J. Po­land: “Ele­ment­ary equi­val­ence and the com­mut­at­or sub­group,” Glas­gow Math. J. 23 : 2 (July 1982), pp. 115–​117. MR 663136 Zbl 0504.​03006 article

[16] L. van den Dries: “A spe­cial­iz­a­tion the­or­em for ana­lyt­ic func­tions on com­pact sets,” In­d­ag. Math. 85 : 4 (December 1982), pp. 391–​396. MR 683526 Zbl 0526.​30004 article

[17] L. van den Dries: “Some ap­plic­a­tions of a mod­el the­or­et­ic fact to (semi-)al­geb­ra­ic geo­metry,” In­d­ag. Math. 85 : 4 (December 1982), pp. 397–​401. MR 683527 Zbl 0538.​14017 article

[18] A. Macintyre, K. McK­enna, and L. van den Dries: “Elim­in­a­tion of quan­ti­fi­ers in al­geb­ra­ic struc­tures,” Adv. Math. 47 : 1 (January 1983), pp. 74–​87. MR 689765 Zbl 0531.​03016 article

[19] E. Con­nell and L. van den Dries: “In­ject­ive poly­no­mi­al maps and the Jac­obi­an con­jec­ture,” J. Pure Ap­pl. Al­gebra 28 : 3 (June 1983), pp. 235–​239. MR 701351 Zbl 0513.​13007 article

[20] L. van den Dries: Re­du­cing to prime char­ac­ter­ist­ic by means of Artin ap­prox­im­a­tion and con­struct­ible prop­er­ties, and ap­plied to Hoch­ster al­geb­ras. Com­mu­nic­a­tions of the Math­em­at­ic­al In­sti­tute, Rijk­suni­versiteit Utrecht 16. Rijk­suni­versiteit Utrecht, 1983. With a pre­face by Jan R. Strook­er. MR 710483 Zbl 0513.​13010 book

[21] L. van den Dries: “Ana­lyt­ic Hardy fields and ex­po­nen­tial curves in the real plane,” Am. J. Math. 106 : 1 (February 1984), pp. 149–​167. MR 729758 Zbl 0597.​26002 article

[22] L. van den Dries and K. Schmidt: “Bounds in the the­ory of poly­no­mi­al rings over fields: A non­stand­ard ap­proach,” In­vent. Math. 76 : 1 (February 1984), pp. 77–​91. MR 739626 Zbl 0539.​13011 article

[23] L. van den Dries: “Al­geb­ra­ic the­or­ies with defin­able Skolem func­tions,” J. Sym­bol­ic Lo­gic 49 : 2 (June 1984), pp. 625–​629. MR 745390 Zbl 0596.​03032 article

[24] L. van den Dries: “Ex­po­nen­tial rings, ex­po­nen­tial poly­no­mi­als and ex­po­nen­tial func­tions,” Pa­cific J. Math. 113 : 1 (1984), pp. 51–​66. MR 745594 Zbl 0603.​13019 article

[25] L. van den Dries and P. Riben­boim: “The ab­so­lute Galois group of a ra­tion­al func­tion field in char­ac­ter­ist­ic zero is a semi­direct product,” Canad. Math. Bull. 27 : 3 (September 1984), pp. 313–​315. MR 749638 Zbl 0548.​12013 article

[26] L. van den Dries and A. J. Wilkie: “Gro­mov’s the­or­em on groups of poly­no­mi­al growth and ele­ment­ary lo­gic,” J. Al­gebra 89 : 2 (August 1984), pp. 349–​374. MR 751150 Zbl 0552.​20017 article

[27] L. van den Dries and H. Levitz: “On Skolem’s ex­po­nen­tial func­tions be­low \( 2^{2^X} \),” Trans. Am. Math. Soc. 286 : 1 (November 1984), pp. 339–​349. MR 756043 Zbl 0556.​03036 article

[28] A. J. Wilkie and L. van den Dries: “An ef­fect­ive bound for groups of lin­ear growth,” Arch. Math. (Basel) 42 : 5 (May 1984), pp. 391–​396. MR 756689 Zbl 0567.​20016 article

[29] L. van den Dries: “Re­marks on Tarski’s prob­lem con­cern­ing \( (\mathbb{R},+,\cdot\,,\operatorname{exp}) \),” pp. 97–​121 in Lo­gic col­loqui­um ’82 (Florence, 23–28 Au­gust 1982). Edi­ted by G. Lolli, G. Longo, and A. Mar­cja. Stud­ies in Lo­gic and the Found­a­tions of Math­em­at­ics 112. North-Hol­land (Am­s­ter­dam), 1984. MR 762106 Zbl 0585.​03006 incollection

[30] L. van den Dries and R. L. Smith: “De­cid­able reg­u­larly closed fields of al­geb­ra­ic num­bers,” J. Sym­bol­ic Lo­gic 50 : 2 (June 1985), pp. 468–​475. MR 793127 Zbl 0574.​12023 article

[31] L. van den Dries: “The field of reals with a pre­dic­ate for the powers of two,” Manusc. Math. 54 : 1–​2 (March 1985), pp. 187–​195. MR 808687 Zbl 0631.​03020 article

[32] L. van den Dries: “A com­plete­ness the­or­em for tri­go­no­met­ric iden­tit­ies and vari­ous res­ults on ex­po­nen­tial func­tions,” Proc. Am. Math. Soc. 96 : 2 (February 1986), pp. 345–​352. MR 818470 Zbl 0619.​03012 article

[33] L. van den Dries: “A gen­er­al­iz­a­tion of the Tarski–Seiden­berg the­or­em, and some nondefin­ab­il­ity res­ults,” Bull. Am. Math. Soc. (N.S.) 15 : 2 (1986), pp. 189–​193. MR 854552 Zbl 0612.​03008 article

[34] L. van den Dries: “Tarski’s prob­lem and Pfaf­fi­an func­tions,” pp. 59–​90 in Lo­gic col­loqui­um ’84 (Manchester, UK, 15–24 Ju­ly 1984). Edi­ted by J. B. Par­is, A. J. Wilkie, and G. M. Wilmers. Stud­ies in Lo­gic and the Found­a­tions of Math­em­at­ics 120. North-Hol­land (Am­s­ter­dam), 1986. MR 861419 Zbl 0616.​03018 incollection

[35] L. van den Dries and P. Riben­boim: “An ap­plic­a­tion of Tarski’s prin­ciple to ab­so­lute Galois groups of func­tion fields,” pp. 131–​148 in Al­gebra and or­der (Lu­miny, France, 1984). Edi­ted by S. Wolfen­stein. Re­search and Ex­pos­i­tion in Math­em­at­ics 14. Hel­d­er­mann (Ber­lin), 1986. MR 891455 Zbl 0645.​12010 incollection

[36] L. van den Dries and P. Riben­boim: “An ap­plic­a­tion of Tarski’s prin­ciple to ab­so­lute Galois groups of func­tion fields,” Ann. Pure Ap­pl. Lo­gic 33 : 1 (1987), pp. 83–​107. MR 870687 Zbl 0645.​12009 article

[37] L. van den Dries: “Al­fred Tarski’s elim­in­a­tion the­ory for real closed fields,” J. Sym­bol­ic Lo­gic 53 : 1 (March 1988), pp. 7–​19. MR 929371 Zbl 0651.​03001 article

[38] L. van den Dries: “Elim­in­a­tion the­ory for the ring of al­geb­ra­ic in­tegers,” J. Reine An­gew. Math. 1988 : 388 (1988), pp. 189–​205. MR 944190 Zbl 0659.​12021 article

[39] J. Denef and L. van den Dries: “\( p \)-ad­ic and real sub­ana­lyt­ic sets,” Ann. Math. (2) 128 : 1 (July 1988), pp. 79–​138. MR 951508 Zbl 0693.​14012 article

[40] L. van den Dries: “On the ele­ment­ary the­ory of re­stric­ted ele­ment­ary func­tions,” J. Sym­bol­ic Lo­gic 53 : 3 (September 1988), pp. 796–​808. MR 960999 Zbl 0698.​03023 article

[41] L. Bélair, L. van den Dries, and A. Macintyre: “Ele­ment­ary equi­val­ence and codi­men­sion in \( p \)-ad­ic fields,” Manuscripta Math. 62 : 2 (June 1988), pp. 219–​225. MR 963007 Zbl 0665.​12027 article

[42] P. Scow­croft and L. van den Dries: “On the struc­ture of semi­al­geb­ra­ic sets over \( p \)-ad­ic fields,” J. Sym­bol­ic Lo­gic 53 : 4 (December 1988), pp. 1138–​1164. MR 973105 Zbl 0692.​14014 article

[43] L. van den Dries, D. Mark­er, and G. Mar­tin: “Defin­able equi­val­ence re­la­tions on al­geb­ra­ic­ally closed fields,” J. Sym­bol­ic Lo­gic 54 : 3 (September 1989), pp. 928–​935. MR 1011180 Zbl 0689.​03019 article

[44] L. van den Dries: “Con­ver­gent series ex­pan­sions of a new type for ex­po­nen­tial func­tions,” Math. Na­chr. 142 (1989), pp. 7–​18. MR 1017368 Zbl 0709.​13011 article

[45] L. van den Dries: “Di­men­sion of defin­able sets, al­geb­ra­ic bounded­ness and Henseli­an fields.” Edi­ted by J. T. Bald­win and A. Mar­cja. Ann. Pure Ap­pl. Lo­gic 45 : 2 (1989), pp. 189–​209. MR 1044124 Zbl 0704.​03017 article

[46] L. P. D. van den Dries: “Weil’s group chunk the­or­em: A to­po­lo­gic­al set­ting,” Ill. J. Math. 34 : 1 (1990), pp. 127–​139. MR 1031890 Zbl 0764.​22001 article

[47] K. McK­enna and L. van den Dries: “Sur­ject­ive poly­no­mi­al maps, and a re­mark on the Jac­obi­an prob­lem,” Manuscripta Math. 67 : 1 (December 1990), pp. 1–​15. MR 1037991 Zbl 0714.​14013 article

[48] L. van den Dries and A. Macintyre: “The lo­gic of Rumely’s loc­al-glob­al prin­ciple,” J. Reine An­gew. Math. 1990 : 407 (1990), pp. 33–​56. MR 1048527 Zbl 0703.​13021 article

[49] L. van den Dries: “A re­mark on Ax’s the­or­em on solv­ab­il­ity mod­ulo primes,” Math. Z. 208 : 1 (December 1991), pp. 65–​70. MR 1125733 Zbl 0744.​11064 article

[50] Z. Chatzida­kis, L. van den Dries, and A. Macintyre: “Defin­able sets over fi­nite fields,” J. Reine An­gew. Math. 1992 : 427 (May 1992), pp. 107–​135. MR 1162433 Zbl 0759.​11045 article

[51] L. van den Dries and J. Holly: “Quan­ti­fi­er elim­in­a­tion for mod­ules with scal­ar vari­ables,” Ann. Pure Ap­pl. Lo­gic 57 : 2 (May 1992), pp. 161–​179. MR 1166465 Zbl 0772.​03017 article

[52] L. van den Dries: “Ana­lyt­ic Ax–Kochen–Er­sov the­or­ems,” pp. 379–​398 in Pro­ceed­ings of the in­ter­na­tion­al con­fer­ence on al­gebra (Nov­os­ibirsk, USSR, 21–26 Au­gust 1989), Part 3. Edi­ted by L. A. Bok­ut, Yu. L. Er­shov, and A. I. Kostrikin. Con­tem­por­ary Math­em­at­ics 131. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1992. Pro­ceed­ings ded­ic­ated to the memory of A. I. Mal­cev. MR 1175894 Zbl 0835.​03004 incollection

[53] C. W. Hen­son, L. A. Ru­bel, L. van den Dries, and M. F. Sing­er: “On the in­teger zer­os of ex­po­nen­tial poly­no­mi­als,” Com­plex Vari­ables The­ory Ap­pl. 23 : 3–​4 (1993), pp. 201–​211. MR 1269635 Zbl 0790.​30003 article

[54] L. van den Dries and C. Miller: “On the real ex­po­nen­tial field with re­stric­ted ana­lyt­ic func­tions,” Is­rael J. Math. 85 : 1–​3 (February 1994), pp. 19–​56. A cor­rec­tion to this art­icle was pub­lished in Is­rael J. Math. 92:1–3 (1995). MR 1264338 Zbl 0823.​03017 article

[55] L. van den Dries, A. Macintyre, and D. Mark­er: “The ele­ment­ary the­ory of re­stric­ted ana­lyt­ic fields with ex­po­nen­ti­ation,” Ann. Math. (2) 140 : 1 (July 1994), pp. 183–​205. MR 1289495 Zbl 0837.​12006 article

[56] L. van den Dries and C. Miller: “Ex­tend­ing Tamm’s the­or­em,” Ann. Inst. Four­i­er (Gren­oble) 44 : 5 (1994), pp. 1367–​1395. MR 1313788 Zbl 0816.​32004 article

[57] L. van den Dries and A. H. Lewen­berg: “\( T \)-con­vex­ity and tame ex­ten­sions,” J. Sym­bol­ic Lo­gic 60 : 1 (March 1995), pp. 74–​102. MR 1324502 Zbl 0856.​03028 article

[58] L. van den Dries: “Para­met­riz­ing the solu­tions of an ana­lyt­ic dif­fer­en­tial equa­tion,” Ill. J. Math. 39 : 3 (1995), pp. 450–​462. Ded­ic­ated to the memory of Lee A. Ru­bel (1928–1995). MR 1339837 Zbl 0845.​34010 article

[59] L. van den Dries and C. Miller: “Cor­rec­tion to: ‘On the real ex­po­nen­tial field with re­stric­ted ana­lyt­ic func­tions’,” Is­rael J. Math. 92 : 1–​3 (February 1995), pp. 427. Cor­rec­tion to an art­icle pub­lished in Is­rael J. Math. 85:1–3 (1994). MR 1357768 Zbl 0973.​03514 article

[60] L. van den Dries and C. Miller: “Geo­met­ric cat­egor­ies and o-min­im­al struc­tures,” Duke Math. J. 84 : 2 (August 1996), pp. 497–​540. MR 1404337 Zbl 0889.​03025 article

[61] L. van den Dries: “o-min­im­al struc­tures on the field of real num­bers,” Jahresber. Deutsch. Math.-Ver­ein. 98 : 3 (1996), pp. 165–​171. MR 1421024 Zbl 0854.​03036 article

[62] L. van den Dries: “o-min­im­al struc­tures,” pp. 137–​185 in Lo­gic: From found­a­tions to ap­plic­a­tions (Keele, UK, 20–29 Ju­ly 1993). Edi­ted by W. Hodges, M. Hy­land, C. Stein­horn, and J. Truss. Ox­ford Sci­ence Pub­lic­a­tions. Ox­ford Uni­versity Press (New York), 1996. European Lo­gic Col­loqui­um. MR 1428004 Zbl 0861.​03028 incollection

[63] L. van den Dries: “\( T \)-con­vex­ity and tame ex­ten­sions, II,” J. Sym­bol­ic Lo­gic 62 : 1 (March 1997), pp. 14–​34. A cor­rec­tion to this art­icle was pub­lished in J. Sym­bol­ic Lo­gic 63:4 (1998). MR 1450511 Zbl 0922.​03055 article

[64] L. van den Dries, A. Macintyre, and D. Mark­er: “Log­ar­ithmic-ex­po­nen­tial power series,” J. Lon­don Math. Soc. (2) 56 : 3 (1997), pp. 417–​434. MR 1610431 Zbl 0924.​12007 article

[65] L. van den Dries and P. Speis­seg­ger: “The real field with con­ver­gent gen­er­al­ized power series,” Trans. Am. Math. Soc. 350 : 11 (1998), pp. 4377–​4421. MR 1458313 Zbl 0905.​03022 article

[66] L. van den Dries: “Dense pairs of o-min­im­al struc­tures,” Fund. Math. 157 : 1 (1998), pp. 61–​78. MR 1623615 Zbl 0906.​03036 article

[67] L. van den Dries: Tame to­po­logy and o-min­im­al struc­tures. Lon­don Math­em­at­ic­al So­ci­ety Lec­ture Note Series 248. Cam­bridge Uni­versity Press, 1998. MR 1633348 Zbl 0953.​03045 book

[68] L. van den Dries: “Cor­rec­tion to: ‘\( T \)-con­vex­ity and tame ex­ten­sions, II’,” J. Sym­bol­ic Lo­gic 63 : 4 (1998), pp. 1597. Cor­rec­tion to an art­icle pub­lished in J. Sym­bol­ic Lo­gic 62:1 (1997). MR 1665787 Zbl 0927.​03068 article

[69] L. van den Dries: “On the ele­ment­ary the­ory of rings of Witt vec­tors with a mul­ti­plic­at­ive set of rep­res­ent­at­ives for the residue field,” Manuscripta Math. 98 : 2 (February 1999), pp. 133–​137. MR 1667599 Zbl 0923.​03053 article

[70] L. van den Dries, D. Haskell, and D. Macph­er­son: “One-di­men­sion­al \( p \)-ad­ic sub­ana­lyt­ic sets,” J. Lon­don Math. Soc. (2) 59 : 1 (1999), pp. 1–​20. MR 1688485 Zbl 0932.​03038 article

[71] L. van den Dries: “o-min­im­al struc­tures and real ana­lyt­ic geo­metry,” pp. 105–​152 in Cur­rent de­vel­op­ments in math­em­at­ics, 1998 (Cam­bridge, MA, 1998). Edi­ted by B. Mazur, W. Schmid, S. T. Yau, D. Jer­is­on, I. M. Sing­er, and D. Stroock. In­ter­na­tion­al Press (Somerville, MA), 1999. MR 1772324 Zbl 0980.​03043 incollection

[72] M. Aschen­bren­ner and L. van den Dries: “Closed asymp­tot­ic couples,” J. Al­gebra 225 : 1 (March 2000), pp. 309–​358. MR 1743664 Zbl 0974.​12015 article

[73] L. van den Dries: “Clas­sic­al mod­el the­ory of fields,” pp. 37–​52 in Mod­el the­ory, al­gebra, and geo­metry. Edi­ted by D. Haskell, A. Pil­lay, and C. Stein­horn. MSRI Pub­lic­a­tions 39. Cam­bridge Uni­versity Press, 2000. MR 1773701 Zbl 0986.​03034 incollection

[74] L. van den Dries and P. Speis­seg­ger: “The field of reals with multisum­mable series and the ex­po­nen­tial func­tion,” Proc. Lon­don Math. Soc. (3) 81 : 3 (2000), pp. 513–​565. MR 1781147 Zbl 1062.​03029 article

[75] L. van den Dries: “An in­ter­me­di­ate value prop­erty for first-or­der dif­fer­en­tial poly­no­mi­als,” pp. 95–​105 in Con­nec­tions between mod­el the­ory and al­geb­ra­ic and ana­lyt­ic geo­metry. Edi­ted by A. Macintyre. Quaderni di Matem­at­ica 6. Aracne (Rome), 2000. MR 1930683 Zbl 0994.​26005 incollection

[76] L. van den Dries and P. Ehr­lich: “Fields of sur­real num­bers and ex­po­nen­ti­ation,” Fund. Math. 167 : 2 (2001), pp. 173–​188. MR 1816044 Zbl 0974.​03035 article

[77] L. van den Dries, A. Macintyre, and D. Mark­er: “Log­ar­ithmic-ex­po­nen­tial series,” pp. 61–​113 in Pro­ceed­ings of the in­ter­na­tion­al con­fer­ence “Ana­lyse & Lo­gique” (Mons, Bel­gi­um, 25–29 Au­gust 1997), published as Ann. Pure Ap­pl. Lo­gic 111 : 1–​2. Issue edi­ted by C. Finet and C. Michaux. July 2001. MR 1848569 Zbl 0998.​12014 incollection

[78] L. van den Dries and P. Ehr­lich: “Er­rat­um to: ‘Fields of sur­real num­bers and ex­po­nen­ti­ation’,” Fund. Math. 168 : 3 (2001), pp. 295–​297. MR 1853411 article

[79] L. van den Dries and F.-V. Kuhl­mann: “Im­ages of ad­dit­ive poly­no­mi­als in \( \mathbb{F}_q(\!(t)\!) \) have the op­tim­al ap­prox­im­a­tion prop­erty,” Canad. Math. Bull. 45 : 1 (2002), pp. 71–​79. MR 1884135 Zbl 1009.​12008 article

[80] M. Aschen­bren­ner and L. van den Dries: “\( H \)-fields and their Li­ouville ex­ten­sions,” Math. Z. 242 : 3 (2002), pp. 543–​588. MR 1985465 Zbl 1066.​12002 article

[81] L. van den Dries and P. Speis­seg­ger: “o-min­im­al pre­par­a­tion the­or­ems,” pp. 87–​116 in Mod­el the­ory and ap­plic­a­tions (Rav­ello, Italy, 27 May–1 June 2002). Edi­ted by L. Bélair, Z. Chatzida­kis, P. D’Aquino, D. Mark­er, M. Otero, F. Point, and A. Wilkie. Quaderni di Matem­at­ica 11. Aracne (Rome), 2002. To An­gus Macintyre, on his 60th birth­day. MR 2159715 Zbl 1081.​03039 incollection

[82] L. van den Dries and A. J. Wilkie: “The laws of in­teger di­vis­ib­il­ity, and solu­tion sets of lin­ear di­vis­ib­il­ity con­di­tions,” J. Symb. Lo­gic 68 : 2 (June 2003), pp. 503–​526. MR 1976588 Zbl 1056.​03020 article

[83] L. van den Dries: “Gen­er­at­ing the greatest com­mon di­visor, and lim­it­a­tions of prim­it­ive re­curs­ive al­gorithms,” Found. Com­put. Math. 3 : 3 (August 2003), pp. 297–​324. MR 1989479 Zbl 1019.​03027 article

[84] L. van den Dries and Y. N. Moschova­kis: “Is the Eu­c­lidean al­gorithm op­tim­al among its peers?,” Bull. Sym­bol­ic Lo­gic 10 : 3 (September 2004), pp. 390–​418. MR 2083290 Zbl 1095.​03025 article

[85] M. Aschen­bren­ner and L. van den Dries: “Li­ouville closed \( H \)-fields,” J. Pure Ap­pl. Al­gebra 197 : 1–​3 (May 2005), pp. 83–​139. MR 2123981 Zbl 1134.​12004 article

[86] M. Aschen­bren­ner and L. van den Dries: “Asymp­tot­ic dif­fer­en­tial al­gebra,” pp. 49–​85 in Ana­lyz­able func­tions and ap­plic­a­tions (Ed­in­burgh, UK, 17–21 June 2002). Edi­ted by O. Costin, M. D. Kruskal, and A. Macintyre. Con­tem­por­ary Math­em­at­ics 373. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2005. MR 2130825 Zbl 1087.​12002 incollection

[87] M. Aschen­bren­ner, L. van den Dries, and J. van der Ho­even: “Dif­fer­en­tially al­geb­ra­ic gaps,” Se­lecta Math. (N.S.) 11 : 2 (December 2005), pp. 247–​280. MR 2183848 Zbl 1151.​12002 article

[88] L. van den Dries and A. Günay­dın: “The fields of real and com­plex num­bers with a small mul­ti­plic­at­ive group,” Proc. Lon­don Math. Soc. (3) 93 : 1 (July 2006), pp. 43–​81. MR 2235481 Zbl 1101.​03028 article

[89] L. van den Dries: “On ex­pli­cit defin­ab­il­ity in arith­met­ic,” pp. 65–​86 in Lo­gic in Tehran (Tehran, 18–22 Oc­to­ber 2003). Edi­ted by A. Enay­at, I. Kalantari, and M. Moniri. Lec­ture Notes in Lo­gic 26. As­so­ci­ation of Sym­bol­ic Lo­gic (La Jolla, CA), 2006. MR 2262314 Zbl 1107.​03042 incollection

[90] L. van den Dries: “Iso­morph­ism of com­plete loc­al No­eth­eri­an rings and strong ap­prox­im­a­tion,” Proc. Am. Math. Soc. 136 : 10 (2008), pp. 3435–​3448. MR 2415027 Zbl 1154.​13006 article

[91] L. van den Dries and Y. N. Moschova­kis: “Arith­met­ic com­plex­ity,” ACM Trans. Com­put. Log. 10 : 1 (2009). Art­icle 2, 49 pp. MR 2537732 Zbl 1367.​68116 article

[92] L. van den Dries and S. Gao: “A Pol­ish group without Lie sums,” Abh. Math. Semin. Univ. Ham­bg. 79 : 1 (June 2009), pp. 135–​147. MR 2541347 Zbl 1181.​22006 article

[93] L. van den Dries and I. Gold­bring: “Loc­ally com­pact con­tract­ive loc­al groups,” J. Lie The­ory 19 : 4 (2009), pp. 685–​695. MR 2598999 Zbl 1222.​22004 ArXiv 0909.​4565 article

[94] L. van den Dries and A. Günay­dın: “Mann pairs,” Trans. Am. Math. Soc. 362 : 5 (2010), pp. 2393–​2414. MR 2584604 Zbl 1192.​03011 article

[95] L. van den Dries and J. Maříková: “Tri­an­gu­la­tion in o-min­im­al fields with stand­ard part map,” Fund. Math. 209 : 2 (2010), pp. 133–​155. MR 2660560 Zbl 1221.​03030 ArXiv 0901.​2339 article

[96] L. van den Dries and V. C. Lopes: “Di­vi­sion rings whose vec­tor spaces are pseudofin­ite,” J. Sym­bol­ic Lo­gic 75 : 3 (September 2010), pp. 1087–​1090. MR 2723784 Zbl 1201.​03021 article

[97] L. van den Dries and I. Gold­bring: “Glob­al­iz­ing loc­ally com­pact loc­al groups,” J. Lie The­ory 20 : 3 (2010), pp. 519–​524. An er­rat­um to this art­icle was pub­lished in J. Lie The­ory 22:2 (2012). MR 2743102 Zbl 1203.​22006 ArXiv 1003.​0963 article

[98] S. Azgin and L. van den Dries: “Ele­ment­ary the­ory of val­ued fields with a valu­ation-pre­serving auto­morph­ism,” J. Inst. Math. Jussieu 10 : 1 (January 2011), pp. 1–​35. MR 2749570 Zbl 1235.​03068 article

[99] L. van den Dries and V. C. Lopes: “In­vari­ant meas­ures on groups sat­is­fy­ing vari­ous chain con­di­tions,” J. Sym­bol­ic Lo­gic 76 : 1 (March 2011), pp. 209–​226. MR 2791344 Zbl 1220.​03024 article

[100] L. van den Dries and A. Günay­dın: “Er­rat­um to ‘Mann pairs’,” Trans. Am. Math. Soc. 363 : 9 (2011), pp. 5057. Er­rat­um to an art­icle pub­lished in Trans. Am. Math. Soc. 362:5 (2010). MR 2806701 Zbl 1227.​03049 article

[101] L. van den Dries and A. Günay­dın: “Defin­able sets in Mann pairs,” Comm. Al­gebra 39 : 8 (2011), pp. 2752–​2763. MR 2834128 Zbl 1243.​03054 article

[102] L. van den Dries and I. Gold­bring: “Er­rat­um to ‘Glob­al­iz­ing loc­ally com­pact loc­al groups’,” J. Lie The­ory 22 : 2 (2012), pp. 489–​490. Er­rat­um to an art­icle pub­lished in J. Lie The­ory 20:3 (2010). MR 2976929 Zbl 1242.​22005 article

[103] M. Aschen­bren­ner, L. van den Dries, and J. van der Ho­even: “To­ward a mod­el the­ory for trans­ser­ies,” Notre Dame J. Form. Log. 54 : 3–​4 (2013), pp. 279–​310. For Anand Pil­lay, on his 60th birth­day. MR 3091660 Zbl 1314.​03037 article

[104] L. van den Dries, J. Koenigs­mann, H. D. Macph­er­son, A. Pil­lay, C. Tof­falori, and A. J. Wilkie: Mod­el the­ory in al­gebra, ana­lys­is and arith­met­ic (Cetraro, Italy, 2–16 Ju­ly 2012). Edi­ted by H. D. Macph­er­son and C. Tof­falori. Lec­ture Notes in Math­em­at­ics 2111. Spring­er (Heidel­berg), 2014. MR 3013956 Zbl 1326.​03045 book

[105] L. van den Dries: “Trun­ca­tion in Hahn fields,” pp. 579–​595 in Valu­ation the­ory in in­ter­ac­tion (Segovia and El Escori­al, Spain, 18–29 Ju­ly 2011). Edi­ted by A. Campillo, F.-V. Kuhl­mann, and B. Teis­si­er. EMS Series of Con­gress Re­ports 10. European Math­em­at­ic­al So­ci­ety (Zürich), 2014. MR 3329048 Zbl 1361.​12004 incollection

[106] L. van den Dries: “Lec­tures on the mod­el the­ory of val­ued fields,” pp. 55–​157 in Mod­el the­ory in al­gebra, ana­lys­is and arith­met­ic (Cetraro, Italy, 2–16 Ju­ly 2012). Edi­ted by H. D. Macph­er­son and C. Tof­falori. Lec­ture Notes in Math­em­at­ics 2111. Spring­er (Ber­lin), 2014. MR 3330198 Zbl 1347.​03074 incollection

[107] L. van den Dries: “Ap­prox­im­ate groups [ac­cord­ing to Hrushovski and Breuil­lard, Green, Tao],” pp. 79–​113 in Sémin­aire Bourbaki: 2013/2014, ex­posés 1074–1088. Astérisque 367–​368. Société Mathématique De France (Par­is), 2015. Ex­posé no. 1077. MR 3363589 Zbl 1358.​11024 incollection

[108] L. van den Dries and I. Gold­bring: “Hil­bert’s 5th prob­lem,” En­sei­gn. Math. 61 : 1–​2 (2015), pp. 3–​43. MR 3449281 Zbl 1335.​22008 article

[109] L. Án­gel and L. van den Dries: “Bounded pregeo­met­ries and pairs of fields,” South Am. J. Log. 2 : 2 (2016), pp. 459–​475. For Fran­cisco Miraglia, on his 70th birth­day. MR 3671046 ArXiv 1707.​03486 article

[110] M. Aschen­bren­ner, L. van den Dries, and J. van der Ho­even: Asymp­tot­ic dif­fer­en­tial al­gebra and mod­el the­ory of trans­ser­ies. An­nals of Math­em­at­ics Stud­ies 195. Prin­ceton Uni­versity Press, 2017. MR 3585498 Zbl 06684722 book

[111] M. Aschen­bren­ner, L. van den Dries, and J. van der Ho­even: “Di­men­sion in the realm of trans­ser­ies,” pp. 23–​39 in Ordered al­geb­ra­ic struc­tures and re­lated top­ics (Lu­miny, France, 12–16 Oc­to­ber 2015). Edi­ted by F. Broglia, F. De­lon, M. Dick­mann, D. Gond­ard-Cozette, and V. A. Powers. Con­tem­por­ary Math­em­at­ics 697. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2017. MR 3716064 Zbl 1388.​12008 ArXiv 1607.​07173 incollection

[112] M. Aschen­bren­ner, L. van den Dries, and J. van der Ho­even: “Max­im­al im­me­di­ate ex­ten­sions of val­ued dif­fer­en­tial fields,” Proc. Lond. Math. Soc. (3) 117 : 2 (April 2018), pp. 376–​406. MR 3851327 Zbl 06929623 article

[113] L. van den Dries and N. Pynn-Coates: “On the unique­ness of max­im­al im­me­di­ate ex­ten­sions of val­ued dif­fer­en­tial fields,” J. Al­gebra 519 (2019), pp. 87–​100. MR 3874517 Zbl 06988683 article

[114] L. van den Dries and P. Ehr­lich: “Ho­mo­gen­eous uni­ver­sal \( H \)-fields,” Proc. Amer. Math. Soc. 147 : 5 (2019), pp. 2231–​2234. MR 3937696 Zbl 07046542 article

[115] M. Aschen­bren­ner, L. van den Dries, and J. van der Ho­even: “The sur­real num­bers as a uni­ver­sal \( H \)-field,” J. Eur. Math. Soc. (JEMS) 21 : 4 (2019), pp. 1179–​1199. MR 3941461 Zbl 1470.​12004 article

[116] L. van den Dries, J. van der Ho­even, and E. Ka­plan: “Log­ar­ithmic hy­per­ser­ies,” Trans. Amer. Math. Soc. 372 : 7 (2019), pp. 5199–​5241. MR 4009458 Zbl 07110652 article