Notes on logic and set theory

Notes on Set Theory

We will now axiomatize set theory. From this point on, we cannot use any previous knowledge of mathematics, aside from providing intuition or motivation. Everyday words such as “finite” or “number” no longer have any technical meaning for us, except as specified by our axioms and definitions. These axioms and definitions will become our entire world, and we must reconstruct mathematics within i...

Notes on Constructive Set Theory

4 Operations on Sets and Classes 25 4.1 Class Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Class Relations and Functions . . . . . . . . . . . . . . . . . . 26 4.3 Some Consequences of Union-Replacement . . . . . . . . . . . 27 4.4 Russell’s paradox . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5 Subset Collection and Exponentiation . . . . . . . . . . . . . . 30...

Logic and Set Theory

Notes on Effective Descriptive Set Theory

Lecture Notes on Descriptive Set Theory

Metric spaces, Borel and analytic sets, Baire property and measurability, dichotomies, equivalence relations. Possible topics: determinacy, group actions, rigidity, turbulence.