J. Robinson :
“An iterative method of solving a game Ann. Math. (2)
54 : 2
(September 1951 ),
pp. 296–301 .
MR
43430 Zbl
0045.08203 article
BibTeX
@article {key43430m,
AUTHOR = {Robinson, Julia},
TITLE = {An iterative method of solving a game},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {54},
NUMBER = {2},
MONTH = {September},
YEAR = {1951},
PAGES = {296--301},
DOI = {10.2307/1969530},
NOTE = {MR:43430. Zbl:0045.08203.},
ISSN = {0003-486X},
}
J. Robinson :
“Existential definability in arithmetic Trans. Am. Math. Soc.
72 : 3
(1952 ),
pp. 437–449 .
MR
48374 Zbl
0047.24802 article
BibTeX
@article {key48374m,
AUTHOR = {Robinson, Julia},
TITLE = {Existential definability in arithmetic},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {72},
NUMBER = {3},
YEAR = {1952},
PAGES = {437--449},
DOI = {10.2307/1990711},
NOTE = {MR:48374. Zbl:0047.24802.},
ISSN = {0002-9947},
}
M. Davis, H. Putnam, and J. Robinson :
“The decision problem for exponential diophantine equations Ann. Math. (2)
74 : 3
(November 1961 ),
pp. 425–436 .
MR
133227 Zbl
0111.01003 article
Abstract
People
BibTeX
We prove that every recursively enumerable set can be existentially defined in terms of exponentiation. Hence, there is no general algorithm for deciding whether or not an exponential diophantine equation has a solution in positive integers. We also obtain a general theorem about bounds for solutions of diophantine equations with a finite number of solution.
@article {key133227m,
AUTHOR = {Davis, Martin and Putnam, Hilary and
Robinson, Julia},
TITLE = {The decision problem for exponential
diophantine equations},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {74},
NUMBER = {3},
MONTH = {November},
YEAR = {1961},
PAGES = {425--436},
DOI = {10.2307/1970289},
NOTE = {MR:133227. Zbl:0111.01003.},
ISSN = {0003-486X},
}
J. Robinson :
“Unsolvable diophantine problems Proc. Am. Math. Soc.
22 : 2
(1969 ),
pp. 534–538 .
MR
244046 Zbl
0182.01901 article
Abstract
BibTeX
We shall show that there is no general method of telling whether an arbitrary polynomial \( P(x_1,\dots \) , \( x_k) \) with integer coefficients is ever a power of 2 for \( x_1,\dots \) , \( x_k \) natural numbers. At present there is no general method known even in the special case with \( k = 1 \) .
Actually we shall show directly that the relation given by \( r = 2^t \) is diophantine in the set \( \mathfrak{I} \) of powers of 2. Hence every recursively enumerable set is diophantine in \( \mathfrak{I} \) by Corollary 5 of Davis, Putnam, and Robinson [1961].
@article {key244046m,
AUTHOR = {Robinson, Julia},
TITLE = {Unsolvable diophantine problems},
JOURNAL = {Proc. Am. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {22},
NUMBER = {2},
YEAR = {1969},
PAGES = {534--538},
DOI = {10.2307/2037095},
NOTE = {MR:244046. Zbl:0182.01901.},
ISSN = {0002-9939},
}
J. Robinson :
“Axioms for number theoretic functions ,”
pp. 253–263
in
Izbrannye voprosy algebry i logiki
[Selected questions of algebra and logic ].
Edited by A. I. Shirshov .
Nauka (Novosibirsk ),
1973 .
Collection dedicated to the memory of A. I. Mal’cev.
MR
329884 Zbl
0279.02035 incollection
People
BibTeX
Anatolii Illarionovich Shirshov
Related
Anatoliĭ Ivanovic Maltsev
Related
@incollection {key329884m,
AUTHOR = {Robinson, Julia},
TITLE = {Axioms for number theoretic functions},
BOOKTITLE = {Izbrannye voprosy algebry i logiki [Selected
questions of algebra and logic]},
EDITOR = {Shirshov, A. I.},
PUBLISHER = {Nauka},
ADDRESS = {Novosibirsk},
YEAR = {1973},
PAGES = {253--263},
NOTE = {Collection dedicated to the memory of
{A}.~{I}. {M}al\cprime cev. MR:329884.
Zbl:0279.02035.},
}
J. Matijasevič and D. Robinson :
“Two universal three-quantifier representations of enumerable sets ,”
pp. 112–123
in
Teopiya algorifmov i matematicheskaya logika
[Theory of algorithms, and mathematical logic ].
Edited by B. A. Kushner and N. M. Nagorny .
Computing Center of the Academy of Sciences (Moscow ),
1974 .
Volume dedicated to A. A. Markov on the occasion of his seventieth birthday.
MR
406780 Zbl
0327.02035 incollection
People
BibTeX
@incollection {key406780m,
AUTHOR = {Matijasevi\v{c}, Juri\u{\i} and Robinson,
D\v{z}ulija},
TITLE = {Two universal three-quantifier representations
of enumerable sets},
BOOKTITLE = {Teopiya algorifmov i matematicheskaya
logika [Theory of algorithms, and mathematical
logic]},
EDITOR = {Kushner, B. A. and Nagorny, N. M.},
PUBLISHER = {Computing Center of the Academy of Sciences},
ADDRESS = {Moscow},
YEAR = {1974},
PAGES = {112--123},
NOTE = {Volume dedicated to {A}.~{A}. {M}arkov
on the occasion of his seventieth birthday.
MR:406780. Zbl:0327.02035.},
}
Y. Matijasevič and J. Robinson :
“Reduction of an arbitrary Diophantine equation to one in 13 unknowns Acta Arith.
27
(1975 ),
pp. 521–553 .
MR
387188 Zbl
0279.10019 article
People
BibTeX
@article {key387188m,
AUTHOR = {Matijasevi\v{c}, Yuri and Robinson,
Julia},
TITLE = {Reduction of an arbitrary {D}iophantine
equation to one in 13 unknowns},
JOURNAL = {Acta Arith.},
FJOURNAL = {Acta Arithmetica. Polska Akademia Nauk.
Instytut Matematyczny},
VOLUME = {27},
YEAR = {1975},
PAGES = {521--553},
DOI = {10.4064/aa-27-1-521-553},
URL = {http://matwbn.icm.edu.pl/ksiazki/aa/aa27/aa27125.pdf},
NOTE = {MR:387188. Zbl:0279.10019.},
ISSN = {0065-1036},
}
M. Davis, Y. Matijasevič, and J. Robinson :
“Hilbert’s tenth problem: Diophantine equations: Positive aspects of a negative solution ,”
pp. 323–378
in
Mathematical developments arising from Hilbert problems
(DeKalb, IL, 13–17 May 1974 ),
Part 2 .
Edited by F. E. Browder .
Proceedings of Symposia in Pure Mathematics 28 .
1976 .
With a loose-leaf erratum.
MR
432534 Zbl
0346.02026 incollection
People
BibTeX
@incollection {key432534m,
AUTHOR = {Davis, Martin and Matijasevi\v{c}, Yuri
and Robinson, Julia},
TITLE = {Hilbert's tenth problem: {D}iophantine
equations: {P}ositive aspects of a negative
solution},
BOOKTITLE = {Mathematical developments arising from
{H}ilbert problems},
EDITOR = {Browder, Felix E.},
VOLUME = {2},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {28},
YEAR = {1976},
PAGES = {323--378},
NOTE = {(DeKalb, IL, 13--17 May 1974). With
a loose-leaf erratum. MR:432534. Zbl:0346.02026.},
ISSN = {0082-0717},
ISBN = {9780821814284},
}
