We build the foundations of set theory using the Zermelo-Fraenkel axioms with choice (ZFC). The material follows the first chapter of Thomas Jech's "Set Theory".
00:00 Introduction
01:10 Overview of the ZFC axioms
10:50 The language of sets
13:29 Classes
18:41 Axiom: Extensionality
20:36 Axiom: Pairing
22:32 Singleton sets and ordered pairs
25:17 Axiom: Separation
29:19 Subclasses of sets are sets
34:51 Axiom: Union
37:50 Axiom: Power set
39:22 Cartesian products
44:05 Relations
49:27 Functions
53:10 Axiom: Infinity
57:32 Axiom: Replacement
1:01:44 Axiom: Regularity
1:06:54 Axiom: Choice
The playlist for the course can be found here: • Logic & Foundations wi...