Two notes on Ackermann's 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...

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.

Lecture Notes on Game Theory Set 3 – Mixed Strategy Equilibria

A game in strategic form does not always have a Nash equilibrium in which each player deterministically chooses one of his strategies. However, players may instead randomly select from among these pure strategies with certain probabilities. Randomizing one’s own choice in this way is called a mixed strategy. A profile of mixed strategies is called a mixed equilibrium if no player can gain on av...