This PDF covers the
following topics related to Set Theory : Introduction, Well-orders and
Ordinals, Classes and Transfinite Recursion, Cardinals, Zorn’s Lemma,
Ramsey’s Theorem, Lo´s’s Theorem, Cumulative Hierarchy, Relativization,
Measurable Cardinals, Godel’s Constructible Universe, Banach-Tarski
Paradox.
This note describes the following topics:
Propositional calculus, Well orderings and ordinals, Posets and Zorns lemma,
Predicate logic, Set theory, Cardinals and incompleteness.
Goal of these notes is to introduce both some of the basic tools in the
foundations of mathematics and gesture toward some interesting philosophical
problems that arise out of them. Topics covered includes: Axioms and
representations, Backbones and problems, advanced set theory.