Publication Date
8-2025
Date of Final Oral Examination (Defense)
6-19-2025
Type of Culminating Activity
Thesis
Degree Title
Master of Science in Mathematics
Department
Mathematics
Supervisory Committee Chair
John Clemens, Ph.D.
Supervisory Committee Member
Randall Holmes, Ph.D.
Supervisory Committee Member
Marion Scheepers, Ph.D.
Abstract
The purpose of reverse mathematics, a field of mathematical logic, is to determine which axioms are required to prove particular mathematical theorems. Gödel's first incompleteness theorem states that within any standard consistent formal system of mathematics, there are statements for which neither themselves nor their negations can be proven. Thus, the goal of reverse mathematics cannot be the discovery of some formal system which underlies all mathematics, which was that of Hilbert's program. Instead, the questions lie in how much mathematical reasoning can be represented and how strong the formal systems are required to be to conduct said reasoning. In this thesis, we will introduce the methods of this discipline through an investigation of the weakened base subsystem of second-order arithmetic, RCA_0^*.
DOI
10.18122/td.2404.boisestate
Recommended Citation
Dvorak, Kaden, "An Introduction to Reverse Mathematics Through the Weakened Base System RCA_0^*." (2025). Boise State University Theses and Dissertations. 2404.
10.18122/td.2404.boisestate