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Arithmetical Problems and Recursively Enumerable Predicates
Arithmetical Problems and Recursively Enumerable Predicates,Journal of Symbolic Logic,Martin Davis
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Arithmetical Problems and Recursively Enumerable Predicates
(
Citations: 13
)
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Martin Davis
Journal:
Journal of Symbolic Logic  JSYML
, vol. 18, no. 1, pp. 3341, 1953
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Citation Context
(5)
...Davis [15,
16
] proposed a strategy for finding such an “unsolvability proof”, which entailed the brave conjecture that all c.e...
S. Barry Cooper
.
Extending and interpreting Post's programme
...In 1950 it was conjectured by Martin Davis [4] (see also [
5
]) that the Diophantine sets were exactly the sets for which there are algorithms for listing their elements (in no particular order and with repetitions allowed in the list)...
George F. McNulty
.
The equational compatibility problem for the real line
...The following is quoted directly from Martin Davis [
5
]...
Grant Olney Passmore
.
Diophantine Sets and Their Decision Problems
...Davis conjectured ([17,
18
]) that this necessary condition is also sufficient:...
...Davis made the first step to proving his conjecture by showing in [
18
] that every effectively enumerable set M has an almost Diophantine representation:...
...To obtain it, Davis started in [
18
] with a representation of the set M by an arbitrary arithmetical formula with any number of bounded universal quantifiers...
...According to a footnote in Davis’s paper [
18
], the idea of obtaining the representation (4) by combining universal quantifiers from a general arithmetic representation was 64 Yuri Matiyasevich...
Yuri Matiyasevich
.
Computation Paradigms in Light of Hilbert's Tenth Problem
...Davis [3], [
4
] proposed that the converse is also true:...
...Martin Davis [
4
] took the first step toward the proof of his conjecture when he obtained an almost Diophantine representation:...
Yu. Matiyasevich
.
Hilbert’s Tenth Problem: Diophantine Equations in the Twentieth Centur...
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Citations
(13)
Extending and interpreting Post's programme
(
Citations: 1
)
S. Barry Cooper
Journal:
Annals of Pure and Applied Logic  APAL
, vol. 161, no. 6, pp. 775788, 2010
Existential arithmetization of Diophantine equations
Yuri Matiyasevich
Journal:
Annals of Pure and Applied Logic  APAL
, vol. 157, no. 23, pp. 225233, 2009
Two universal 3quantifier representations of recursively enumerable sets
(
Citations: 5
)
Yuri Matiyasevich
,
Julia Robinson
Published in 2008.
The equational compatibility problem for the real line
George F. McNulty
Journal:
Algebra Universalis  ALGEBRA UNIV
, vol. 59, no. 3, pp. 257275, 2008
Diophantine Sets and Their Decision Problems
Grant Olney Passmore
Published in 2007.