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A note on effective ultrapowers: Uniform failure of bounded collection

✍ Scribed by Thomas McLaughlin

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
302 KB
Volume
39
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

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.

📜 SIMILAR VOLUMES

A note on the Σ1 collection scheme and f
A note on the Σ1 collection scheme and fragments of bounded arithmetic
✍ Zofia Adamowicz; Leszek Aleksander Kołodziejczyk 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 115 KB

Bounded arithmetic, collection principle, weak pigeonhole principle. ## MSC (2000) 03F30 We show that for each n ≥ 1, if T n 2 does not prove the weak pigeonhole principle for Σ b n functions, then the collection scheme BΣ1 is not finitely axiomatizable over T n 2 . The same result holds with S n