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On two problems concerning end extensions

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Abstract

We study problems of Clote and Paris, concerning the existence of end extensions of models of Σ n -collection. We continue the study of the notion of ‘Γ-fullness’, begun by Wilkie and Paris (Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North- Holland, Amsterdam, 1989) and introduce and study a generalization of it, to be used in connection with the existence of Σ n -elementary end extensions (instead of plain end extensions). We obtain (a) alternative proofs of results (Adamowicz in Fund. Math. 136, 133–145, 1990) and (Wilkie and Paris in Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North-Holland, Amsterdam, 1989) related to the problem of Paris and (b) a partial solution to the problem of Clote.

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Correspondence to C. Dimitracopoulos.

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Research partially supported by INTAS grant 2000-447 and grant 70/4/5633 of the University of Athens Research Secretariat.

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Cornaros, C., Dimitracopoulos, C. On two problems concerning end extensions. Arch. Math. Logic 47, 1–14 (2008). https://doi.org/10.1007/s00153-007-0055-1

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