Arithmetical classification of the set of all provably recursive functions

Vítězslav Švejdar

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 4, page 631-634
  • ISSN: 0010-2628

Abstract

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The set of all indices of all functions provably recursive in any reasonable theory T is shown to be recursively isomorphic to U × U ¯ , where U is Π 2 -complete set.

How to cite

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Švejdar, Vítězslav. "Arithmetical classification of the set of all provably recursive functions." Commentationes Mathematicae Universitatis Carolinae 40.4 (1999): 631-634. <http://eudml.org/doc/248443>.

@article{Švejdar1999,
abstract = {The set of all indices of all functions provably recursive in any reasonable theory $T$ is shown to be recursively isomorphic to $U\times \overline\{U\}$, where $U$ is $\Pi _2$-complete set.},
author = {Švejdar, Vítězslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {provable; recursive; complete; recursive; provable; complete},
language = {eng},
number = {4},
pages = {631-634},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Arithmetical classification of the set of all provably recursive functions},
url = {http://eudml.org/doc/248443},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Švejdar, Vítězslav
TI - Arithmetical classification of the set of all provably recursive functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 4
SP - 631
EP - 634
AB - The set of all indices of all functions provably recursive in any reasonable theory $T$ is shown to be recursively isomorphic to $U\times \overline{U}$, where $U$ is $\Pi _2$-complete set.
LA - eng
KW - provable; recursive; complete; recursive; provable; complete
UR - http://eudml.org/doc/248443
ER -

References

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  1. Buss S.R., Bounded Arithmetic, Bibliopolis, Napoli, 1986. Zbl1148.03038MR0880863
  2. Hájek P., Pudlák P., Metamathematics of First Order Arithmetic, Springer, 1993. MR1219738
  3. Hay L., Index sets universal for differences of arithmetic sets, Zeitschr. f. math. Logik und Grundlagen d. Math. 20 (1974), 239-254. (1974) Zbl0311.02052MR0429518
  4. Kaye R., Models of Peano Arithmetic, Oxford University Press, 1991. Zbl1020.03065MR1098499
  5. Kirby L.A.S., Paris J.B., Accessible independence results for Peano arithmetic, Bull. London Math. Soc. 14 285-293 (1982). (1982) Zbl0501.03017MR0663480
  6. Lewis F.D., Classes of recursive functions and their index sets, Zeitschr. f. math. Logik und Grundlagen d. Math. 17 291-294 (1971). (1971) Zbl0229.02035MR0294130
  7. Odifreddi P., Classical Recursion Theory, North-Holland, Amsterdam, 1989. Zbl0931.03057MR0982269
  8. Paris J.B., Harrington L., A mathematical incompleteness in Peano arithmetic, in J. Barwise, editor, Handbook of Mathematical Logic, Chapter D8., North-Holland, 1977. MR0457132
  9. Rogers H., Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, 1967. Zbl0256.02015MR0224462

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