Extensions And Corollaries of Recent Work On Hilberts Tenth Problem
Extensions And Corollaries of Recent Work On Hilberts Tenth Problem
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/iccii^ [(b^jsjq, .^*m^»""V lioanxao „, ^ 1 •• • • t r r « . ^ U - . 5:. . V. . O'jCi) A •rf^ef. E--" C2 fi'. S 0^:/' 8 Lernjiia 7. Let S be a recursively enuraerable set. Then, there is a pol^mornial P such that: ^ = ^' V V V x^, ... , x^ Y^, . , . , J^ 2^, ... , Z^ i% "^ Proof . This lemma is essentially a restatement of the main result of [2], namely that every recursively enumerable set is exponential Diophantlne, The theorem now follows at once from Lemmas 6 and 7.
al. Va s-C' I" Di-'-... ■ •■' ' ■ -r . L d p.. N:-:. NeJ. U'. ':!- . -1 won al Footnotes 1. Cf. [1] or [3].
2. Cf. [3] and [6].
3. However, we are follox->ring [2] rather than [51 in taking variables to have the positive integers (rather than the non-negative integers) as their range, 4. [... ] here means, as usual, "the greatest integer = ... , " .. ( ■'• --r- 10 References [1] Martin Davis, Computability and unsolvability, McGraw-Hill, 1958.
[2. ] Martin Davis, Hilary Putnam, and Julia Robinson, The decision problem for exioonential Diophantine equations.
What to read after Extensions And Corollaries of Recent Work On Hilberts Tenth Problem?
You can find similar books in the "Read Also" column, or choose other free books by Martin Davis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
[?.
/iccii^ [(b^jsjq, .^*m^»""V lioanxao „, ^ 1 •• • • t r r « . ^ U - . 5:. . V. . O'jCi) A •rf^ef. E--" C2 fi'. S 0^:/' 8 Lernjiia 7. Let S be a recursively enuraerable set. Then, there is a pol^mornial P such that: ^ = ^' V V V x^, ... , x^ Y^, . , . , J^ 2^, ... , Z^ i% "^ Proof . This lemma is essentially a restatement of the main result of [2], namely that every recursively enumerable set is exponential Diophantlne, The theorem now follows at once from Lemmas 6 and 7.
al. Va s-C' I" Di-'-... ■ •■' ' ■ -r . L d p.. N:-:. NeJ. U'. ':!- . -1 won al Footnotes 1. Cf. [1] or [3].
2. Cf. [3] and [6].
3. However, we are follox->ring [2] rather than [51 in taking variables to have the positive integers (rather than the non-negative integers) as their range, 4. [... ] here means, as usual, "the greatest integer = ... , " .. ( ■'• --r- 10 References [1] Martin Davis, Computability and unsolvability, McGraw-Hill, 1958.
[2. ] Martin Davis, Hilary Putnam, and Julia Robinson, The decision problem for exioonential Diophantine equations.
What to read after Extensions And Corollaries of Recent Work On Hilberts Tenth Problem?
You can find similar books in the "Read Also" column, or choose other free books by Martin Davis to read onlineMoreLess
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