This note explains the following
topics: The language of set theory and well-formed formulas, Classes vs. Sets,
Notational remarks, Some axioms of ZFC and their elementary, Consequences, From
Pairs to Products, Relations, Functions, Products and sequences, Equivalence
Relations and Order Relations, Equivalence relations, partitions and
transversals, A Game of Thrones, Prisoners and Hats, Well-orders, Well-founded
relations and the Axiom of Foundation, Natural Numbers, The construction of the
set of natural numbers, Arithmetic on the set of natural numbers, Equinumerosity,
Finite sets, To infinity and beyond, Construction of various number systems,
Integers, Rational numbers, Real numbers, Ordinal numbers.
This note describes the following topics:
Propositional calculus, Well orderings and ordinals, Posets and Zorns lemma,
Predicate logic, Set theory, Cardinals and incompleteness.
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.
This note explains the following
topics: The language of set theory and well-formed formulas, Classes vs. Sets,
Notational remarks, Some axioms of ZFC and their elementary, Consequences, From
Pairs to Products, Relations, Functions, Products and sequences, Equivalence
Relations and Order Relations, Equivalence relations, partitions and
transversals, A Game of Thrones, Prisoners and Hats, Well-orders, Well-founded
relations and the Axiom of Foundation, Natural Numbers, The construction of the
set of natural numbers, Arithmetic on the set of natural numbers, Equinumerosity,
Finite sets, To infinity and beyond, Construction of various number systems,
Integers, Rational numbers, Real numbers, Ordinal numbers.
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.