Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 55, Number 2 (2014), 231-244.
Combinatorial Unprovability Proofs and Their Model-Theoretic Counterparts
For a function with domain , where , we say that is canonical for if there is a such that for any and in , iff for all . The canonical Ramsey theorem is the statement that for any , if , then there is an infinite canonical for . 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 .
Notre Dame J. Formal Logic, Volume 55, Number 2 (2014), 231-244.
First available in Project Euclid: 24 April 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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