Variants of the chain-antichain principle in reverse mathematics

Abstract

Restricting the chain-antichain principle CAC to partially ordered sets which respect the natural ordering of the integers is a trivial distinction in the sense of classical reverse mathematics. We utilize computability-theoretic reductions to formally establish distinguishing characteristics of CAC and the aforementioned restriction to elaborate on the apparent differences obfuscated over RCA0. Stable versions of both principles are also analyzed in this way.