Truth in generic cuts

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

Abstract

In an earlier paper (MLQ 54,129-144) the first author initiated the study of generic cuts of a model of Peano arithmetic relative to a notion of an indicator in the model. This paper extends that work. We generalise the idea of an indicator to a related neighbourhood system; this allows the theory to be extended to one that includes the case of elementary cuts. Most results transfer to this more general context, and in particular we obtain the idea of a generic cut relative to a neighbourhood system, which is studied in more detail. The main new result on generic cuts presented here is a description of truth in the structure (M. I), where 1 is a generic cut of a model M of Peano arithmetic. The special case of elementary generic cuts provides a partial answer to a question of Kossak [R. Kossak, Four problems concerning recursively saturated models of arithmetic, Notre Dame Journal of Formal Logic 36(4) (1995) 519-530]. (C) 2010 Published by Elsevier B.V.

Details

Original languageEnglish
Pages (from-to)987-1005
Number of pages19
JournalAnnals of Pure and Applied Logic
Volume161
Issue number8
Publication statusPublished - 1 May 2010

Keywords

  • Peano arithmetic, Generic cuts