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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 and Forcing Lecture Notes by Jean louis Krivine
This PDF covers the following topics related to Set Theory and Forcing : Introduction, Axioms of Set Theory, Class Relations, Functions, Families of Sets and Cartesian Products, Ordinals and Cardinals, Classes and Sets, Well-Orderings and Ordinals, Inductive Definitions, Stratified or Ranked Classes, Ordinal Arithmetic, Cardinals and Their Arithmetic, Foundation, Relativization, Consistency of the Axiom of Foundation, Inaccessible Ordinals and Models of ZFC, The Reflection Scheme, Formalizing Logic in U, Model Theory for U-formulas, Ordinal Definability and Inner Models of ZFC, The Principle of Choice, Constructibility , Formulas and Absoluteness, The Generalized Continuum Hypothesis in L, Forcing, Generic Extensions, Mostowski Collpase of a Well-founded Relation, Construction of Generic Extensions, Definition of Forcing, etc.
Author(s): Jean-louis Krivine
65 Pages
Descriptive Set Theory by David Marker
This note covers the following topics: Classical Descriptive Set Theory, Polish Spaces, Borel Sets, Effective Descriptive Set Theory: The Arithmetic Hierarchy, Analytic Sets, Coanalytic Sets, Determinacy, Hyperarithmetic Sets, Borel Equivalence Relations, Equivalence Relations, Tame Borel Equivalence Relations, Countable Borel Equivalence Relations, Hyperfinite Equivalence Relations.
Author(s): David Marker
105 Pages
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
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