Skip to main content Accessibility help
×
Home

On external Scott algebras in nonstandard models of Peano arithmetic

  • Vladimir Kanovei (a1)

Abstract

We prove that a necessary and sufficient condition for a countable set of sets of integers to be equal to the algebra of all sets of integers definable in a nonstandard elementary extension of ω by a formula of the PA language which may include the standardness predicate but does not contain nonstandard parameters, is as follows: is closed under arithmetical definability and contains 0(ω) the set of all (Gödel numbers of) true arithmetical sentences.

Some results related to definability of sets of integers in elementary extensions of ω are included.

Copyright

References

Hide All
[1]Harrington, L., The constructible reals can be anything, a preprint dated May 1974 with several addendums dated up to 10 1975.
[2]Hinman, P., Recursion theoretic hierarchies, Springer-Verlag, Berlin, 1978.
[3]Kanovei, V., The set of all analytically definable sets of natural numbers can be defined analytically, Mathematics of the USSR-Izvestiya, vol. 15 (1980), pp. 469500.
[4]Kaye, R. W., Models of Peano arithmetic, Oxford logic guides, vol. 15, Oxford Science Publications, 1991.
[5]Scott, D., Algebras of sets binumerable in complete extensions of arithmetic, Recursive function theory, Proceedings of the Fifth Symposium in Pure Mathematics of the American Mathematical Society, 1962, pp. 117121.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed