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2014 Combinatorial Unprovability Proofs and Their Model-Theoretic Counterparts
Mojtaba Aghaei, Amir Khamseh
Notre Dame J. Formal Logic 55(2): 231-244 (2014). DOI: 10.1215/00294527-2420654

Abstract

For a function f with domain [X]n, where XN, we say that HX is canonical for f if there is a υn such that for any x0,,xn1 and y0,,yn1 in H, f(x0,,xn1)=f(y0,,yn1) iff xi=yi for all iυ. The canonical Ramsey theorem is the statement that for any nN, if f:[N]nN, then there is an infinite HN canonical for f. This paper is concerned with a model-theoretic study of a finite version of the canonical Ramsey theorem with a largeness condition and also a version of the Kanamori–McAloon principle. As a consequence, we produce new indicators for cuts satisfying PA.

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Mojtaba Aghaei. Amir Khamseh. "Combinatorial Unprovability Proofs and Their Model-Theoretic Counterparts." Notre Dame J. Formal Logic 55 (2) 231 - 244, 2014. https://doi.org/10.1215/00294527-2420654

Information

Published: 2014
First available in Project Euclid: 24 April 2014

zbMATH: 1301.03062
MathSciNet: MR3201834
Digital Object Identifier: 10.1215/00294527-2420654

Subjects:
Primary: 03F30
Secondary: 03B30 , 03C62

Keywords: canonical Ramsey theorem , Kanamori–McAloon principle , Paris–Harrington principle , unprovable statements

Rights: Copyright © 2014 University of Notre Dame

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Vol.55 • No. 2 • 2014
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