Set theory
is the branch of mathematical logic that studies sets, which informally are
collections of objects. Topics covered includes: The Axioms of Set Theory, The
Natural Numbers, The Ordinal Numbers, Relations and Orderings, Cardinality,
There Is Nothing Real About The Real Numbers, The Universe, Reflection,
Elementary Submodels and Constructibility.
This PDF covers
the following topics related to Set Theory : General considerations, Basic
concepts, Constructions in set theory, Relations and functions, Number
systems and set theory, Infinite constructions in set theory, The Axiom of
Choice and related properties, Set theory as a foundation for mathematics.
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.