Title of the course: Axiom of Choice: its mathematics and philosophy
Instructor: Assoc. Prof. Ahmet Çevik
Institution: JSGA/ODTÜ
Dates: 26-31 August 2024
Prerequisites: Some background in logic and sets
Level: Advanced undergraduate, graduate
Abstract: The Axiom of Choice is one of the most essential and fruitful axioms of ZFC set theory which has been widely studied by the mathematical and philosophical community. In this lecture series, we will delve into details about the Axiom of Choice, concerning its origins, mathematical and philosophical relevance, and its consequences. We will start by giving a short history of the axiom to see how it emerged from Zermelo’s proofs. We will then look at the criticisms made by the constructivists, and then demonstrate its importance and applications in mathematics. We will finally argue whether or not the Axiom of Choice is indispensable for mathematics, and give supporting statements in favour of its naturality. The course will address to advanced undergraduates as well as graduate students who are interested in the foundations of mathematics.
Language: TR, EN