Notre Dame Journal of Formal Logic

Combinatorial Unprovability Proofs and Their Model-Theoretic Counterparts

Mojtaba Aghaei and Amir Khamseh

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 55, Number 2 (2014), 231-244.

Dates
First available in Project Euclid: 24 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1398345782

Digital Object Identifier
doi:10.1215/00294527-2420654

Mathematical Reviews number (MathSciNet)
MR3201834

Zentralblatt MATH identifier
1301.03062

Subjects
Primary: 03F30: First-order arithmetic and fragments
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 03C62: Models of arithmetic and set theory [See also 03Hxx]

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

Citation

Aghaei, Mojtaba; Khamseh, Amir. Combinatorial Unprovability Proofs and Their Model-Theoretic Counterparts. Notre Dame J. Formal Logic 55 (2014), no. 2, 231--244. doi:10.1215/00294527-2420654. https://projecteuclid.org/euclid.ndjfl/1398345782


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