Set Theory by University of California Riverside

Set Theory by Victoria University of Wellington

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.

Author(s): Victoria University of Wellington

60 Pages

Set Theory by University of California Riverside

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.

Author(s): University of California Riverside

214 Pages

Set Theory by Burak Kaya

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.

Author(s): Burak Kaya

91 Pages

Lectures On Set Theory

This note covers the following topics: Logic, Elementary Set Theory, Generic Sets And Forcing, Infinite Combinatorics, Pcf, Continuum Cardinals.

Author(s): J. Donald Monk

602 Pages