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 .
"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