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A note on effective ultrapowers: Uniform failure of bounded collection
Author(s) -
McLaughlin Thomas
Publication year - 1993
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19930390146
Subject(s) - ultraproduct , argument (complex analysis) , mathematics , bounded function , arithmetic , discrete mathematics , calculus (dental) , medicine , mathematical analysis , dentistry
By suitably adapting an argument of Hirschfeld (see [2, Chapter 9]), we show that there is a single Δ 1 formula that defeats “bounded collection” for any model of II 2 Arithmetic that is either a recursive ultrapower or an existentially complete model. Some related facts are noted. MSC: 03F30, 03C62.
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