EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 52(66), pp. 1--4 (1992)

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Fragments of complete extensions of PA and McDowell--Specker's theorem

Ilijas Farah

Matemativki fakultet, Beograd, Yugoslavia

Abstract: 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 end-extension.) This is accomplished using a model called $\Sigma_n$-atomic. This result can be interpreted as ``McDowell--Specker's Theorem does not hold for $\Sigma_n$-fragments of {\bf PA}''.

Classification (MSC2000): 03C20, 03C62

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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
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