Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Logic and Foundations
Reverse Mathematics Of Ramsey's Theorem, Nikolay Maslov
Reverse Mathematics Of Ramsey's Theorem, Nikolay Maslov
Electronic Theses, Projects, and Dissertations
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 …
On The Logic Of Reverse Mathematics, Alaeddine Saadaoui
On The Logic Of Reverse Mathematics, Alaeddine Saadaoui
Theses, Dissertations and Capstones
The goal of reverse mathematics is to study the implication and non-implication relationships between theorems. These relationships have their own internal logic, allowing some implications and non-implications to be derived directly from others. The goal of this thesis is to characterize this logic in order to capture the relationships between specific mathematical works. The results of our study are a finite set of rules for this logic and the corresponding soundness and completeness theorems. We also compare our logic with modal logic and strict implication logic. In addition, we explain two applications of S-logic in topology and second order arithmetic.