PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 52(66), pp. 14 (1992) 

Fragments of complete extensions of PA and McDowellSpecker's theoremIlijas FarahMatemativki fakultet, Beograd, YugoslaviaAbstract: We generalise Theorem 1.4 of [2] and prove that for every complete extension {\bf T} of {\bf PA} and any $n\in\omega$ there exists a model for $\Sigma_n$fragment of {\bf T} that is not extendable (that is, a model with no proper strong elementary endextension.) This is accomplished using a model called $\Sigma_n$atomic. This result can be interpreted as ``McDowellSpecker's Theorem does not hold for $\Sigma_n$fragments of {\bf PA}''. Classification (MSC2000): 03C20, 03C62 Full text of the article:
Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
