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An Introduction To Set Theory
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.
Author(s): Professor William A. R. Weiss
119 Pages 
These notes are meant as an introduction to descriptive set theor y. This book contains below topics, Borel Sets and the Borel Hierarchy, Analytic Sets, Reductions, Uniformization.
Author(s): Matthew Foreman
55 Pages
This book contains below topics, and discuss how Boolean ultr apowers can be applied in urelement set theory, ZFCU R Collection A, Over ZFUR, for every cardinal, the following are equivalent, DC scheme, If duplication holds over A A, then homogeneity holds over A, Assume Tail and AC A Duplication holds over some set of urelements, Over ZFCUR, the following implications hold, DC Ord Collection, RP Collection.
Author(s): Bokai Yao
114 Pages
This note describes the following topics, Propositional calculus, Well orderings and ordinals, Posets and Zorns lemma, Predicate logic, Set theory, Cardinals and incompleteness.
Author(s): I B Leader
70 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, WellOrderings 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 Uformulas, 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 Wellfounded Relation, Construction of Generic Extensions, Definition of Forcing, etc.
Author(s): Jean-louis Krivine
65 Pages
Set Theory by Victoria University of Wellington
This PDF covers the following topics related to Set Theory, Introduction, Wellorders and Ordinals, Classes and Transfinite Recursion, Cardinals, Zorns Lemma, Ramseys Theorem, Loss Theorem, Cumulative Hierarchy, Relativization, Measurable Cardinals, Godels Constructible Universe, BanachTarski Paradox.
Author(s): Victoria University of Wellington
60 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 wellformed 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, Wellorders, Wellfounded 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
Set Theory for Computer Science
The aim is to introduce fundamental concepts and techniques in set theory in preparation for its many applications in computer science. Topics covered includes, Mathematical argument, Sets and Logic, Relations and functions, Constructions on sets, Inductive definitions, Wellfounded induction, Inductivelydefined classes and FraenkelMostowski sets.
Author(s): Glynn Winskel
141 Pages