Olivetti Club

Hanul JeonCornell University
Consequences of the axiom of choice

Tuesday, February 22, 2022 - 4:35pm
Malott 406

The Axiom of Choice (AC) is a powerful axiom for proving existence claims. However, its non-constructive nature brought a controversy about whether AC is acceptable or not, which ended up with Gödel and Cohen's independence result on AC. In this expository talk, I will provide some weak variants of AC, and the consequences of AC and its variants in other fields. If time permits, I will describe how to prove a given statement is not provable without AC. I will assume the listeners are familiar with elementary set theory, but no prerequisite about ordinals and cardinals is required.

Refreshments will be served in the lounge at 4:00 PM.