Date of Award
Master of Arts in Mathematics
First Reader/Committee Chair
Reverse mathematics aims to determine which set theoretic axioms are necessary to prove the theorems outside of the set theory. Since the 1970’s, there has been an interest in applying reverse mathematics to study combinatorial principles like Ramsey’s theorem to analyze its strength and relation to other theorems. Ramsey’s theorem for pairs states that for any infinite complete graph with a finite coloring on edges, there is an infinite subset of nodes all of whose edges share one color. In this thesis, we introduce the fundamental terminology and techniques for reverse mathematics, and demonstrate their use in proving Kőnig's lemma and Ramsey's theorem over RCA0.
Maslov, Nikolay, "Reverse Mathematics of Ramsey's Theorem" (2023). Electronic Theses, Projects, and Dissertations. 1651.