L. van den Dries :
“Some model theory and number theory for models of weak systems of arithmetic 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
People
BibTeX
@incollection {key606793m,
AUTHOR = {van den Dries, Lou},
TITLE = {Some model theory and number theory
for models of weak systems of arithmetic},
BOOKTITLE = {Model theory of algebra and arithmetic},
EDITOR = {Pacholski, L. and Wierzejewski, J. and
Wilkie, A. J.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {834},
PUBLISHER = {Springer},
YEAR = {1980},
PAGES = {346--362},
DOI = {10.1007/BFb0090173},
NOTE = {(Karpacz, Poland, 1--7 September 1979).
MR:606793. Zbl:0454.03034.},
ISSN = {0075-8434},
ISBN = {9783540102694},
}
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
People
BibTeX
@article {key751150m,
AUTHOR = {van den Dries, L. and Wilkie, A. J.},
TITLE = {Gromov's theorem on groups of polynomial
growth and elementary logic},
JOURNAL = {J. Algebra},
FJOURNAL = {Journal of Algebra},
VOLUME = {89},
NUMBER = {2},
MONTH = {August},
YEAR = {1984},
PAGES = {349--374},
DOI = {10.1016/0021-8693(84)90223-0},
NOTE = {MR:751150. Zbl:0552.20017.},
ISSN = {0021-8693},
}
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
People
BibTeX
@article {key756689m,
AUTHOR = {Wilkie, A. J. and van den Dries, L.},
TITLE = {An effective bound for groups of linear
growth},
JOURNAL = {Arch. Math. (Basel)},
FJOURNAL = {Archiv der Mathematik},
VOLUME = {42},
NUMBER = {5},
MONTH = {May},
YEAR = {1984},
PAGES = {391--396},
DOI = {10.1007/BF01190686},
NOTE = {MR:756689. Zbl:0567.20016.},
ISSN = {0003-889X},
}
L. van den Dries :
“Tarski’s problem and Pfaffian functions 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
Abstract
People
BibTeX
The introduction outlines the subject in precise but nontechnical terms. In the remainder of the paper we go into details on some points, prove various partial results, and show how our main goal, the Decomposition Conjecture, reduces to a technical question on sets of asymptotes. Many open problems and observations not directly related to the Decomposition Conjecture are scattered throughout the text. Complete proofs of the facts discussed will appear elsewhere.
@incollection {key861419m,
AUTHOR = {van den Dries, Lou},
TITLE = {Tarski's problem and {P}faffian functions},
BOOKTITLE = {Logic colloquium '84},
EDITOR = {Paris, J. B. and Wilkie, A. J. and Wilmers,
G. M.},
SERIES = {Studies in Logic and the Foundations
of Mathematics},
NUMBER = {120},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1986},
PAGES = {59--90},
DOI = {10.1016/S0049-237X(08)70457-9},
NOTE = {(Manchester, UK, 15--24 July 1984).
MR:861419. Zbl:0616.03018.},
ISSN = {0049-237X},
ISBN = {9780444879998},
}
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
People
BibTeX
@incollection {key2159715m,
AUTHOR = {van den Dries, L. and Speissegger, P.},
TITLE = {o-minimal preparation theorems},
BOOKTITLE = {Model theory and applications},
EDITOR = {B\'elair, L. and Chatzidakis, Z. and
D'Aquino, P. and Marker, D. and Otero,
M. and Point, F. and Wilkie, A.},
SERIES = {Quaderni di Matematica},
NUMBER = {11},
PUBLISHER = {Aracne},
ADDRESS = {Rome},
YEAR = {2002},
PAGES = {87--116},
NOTE = {(Ravello, Italy, 27 May--1 June 2002).
To Angus Macintyre, on his 60th birthday.
MR:2159715. Zbl:1081.03039.},
ISSN = {2420-8450},
ISBN = {9788879994118},
}
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
Abstract
People
BibTeX
@article {key1976588m,
AUTHOR = {van den Dries, L. and Wilkie, A. J.},
TITLE = {The laws of integer divisibility, and
solution sets of linear divisibility
conditions},
JOURNAL = {J. Symb. Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {68},
NUMBER = {2},
MONTH = {June},
YEAR = {2003},
PAGES = {503--526},
DOI = {10.2178/jsl/1052669061},
NOTE = {MR:1976588. Zbl:1056.03020.},
ISSN = {0022-4812},
}
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
People
BibTeX
@book {key3013956m,
AUTHOR = {van den Dries, Lou and Koenigsmann,
Jochen and Macpherson, H. Dugald and
Pillay, Anand and Toffalori, Carlo and
Wilkie, Alex J.},
TITLE = {Model theory in algebra, analysis and
arithmetic},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {2111},
PUBLISHER = {Springer},
ADDRESS = {Heidelberg},
YEAR = {2014},
PAGES = {viii+195},
NOTE = {(Cetraro, Italy, 2--16 July 2012). Edited
by H. D. Macpherson
and C. Toffalori. MR:3013956.
Zbl:1326.03045.},
ISSN = {0075-8434},
ISBN = {9783642549359},
}
