

This section contains free ebooks and guides on Set Theory, some of the resources in this section can be viewed online and some of them can be downloaded.




Introduction to Modern Set TheoryJudith RoitmanPDF  129 Pages  EnglishThis note is aimed at two
audiences students who are interested in studying set theory for its own sake,
and students in other areas who may be curious about applications of set theory
to their field. Topics covered includes: Partially ordered sets, Equivalence
relations , Theories and their models, The axioms, Regularity and choice,
Embedding mathematics into set theory, Infinite numbers, Two models of set
theory, Semiadvanced set theory.
 Set Theory Some Basics And A Glimpse Of Some Advanced TechniquesToby
MeadowsPDF  91 Pages  EnglishGoal 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.
 Lectures On Set TheoryJ. Donald MonkPDF  602 Pages  EnglishThis note covers the following topics:
Logic, Elementary Set Theory, Generic Sets And Forcing, Infinite Combinatorics,
Pcf, Continuum Cardinals.
 Set Theory by Anush TserunyanAnush TserunyanOnline  NA Pages  EnglishThis note is an
introduction to the Zermelo–Fraenkel set theory with Choice (ZFC). Topics
covered includes: The axioms of set theory , Ordinal and cardinal arithmetic,
The axiom of foundation, Relativisation, absoluteness, and reflection, Ordinal
definable sets and inner models of set theory, The constructible universe L
Cohen's method of forcing, Independence of the axiom of choice and the continuum
hypothesis.
 An Introduction To Set TheoryProfessor William A. R. WeissPDF  119 Pages  EnglishSet 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.
 Set Theory for Computer ScienceGlynn WinskelPDF  141 Pages  EnglishThe 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.
 The Axioms of Set TheoryThomas ForsterPDF  98 Pages  EnglishThis note covers the following topics:
The Cumulative Hierarchy, Some Philosophical Prolegomena, Listing the Axioms,
First Bundle: The Axiom of Extensionality, Second Bundle: The Closure Axioms,
Third Bundle: The Axioms of infinity, Replacement and Collection.
 Set theory and the structure of arithmeticNorman T HamiltonOnline  286 Pages  EnglishThe
purposes of this book is, first, to answer the question 'What is a number?' and,
of greater importance, to provide a foundation for the study of abstract
algebra, elementary Euclidean geometry and analysis. This book covers the
following topics: The elements of the theory of sets, The Natural Numbers, The
Integers and the Rational Numbers and the Real Numbers.
 A Problem Course in Mathematical Logic  Background and Fundamentals of MathematicsEdwin
H.ConnellOnline  NA Pages  EnglishThis note covers the following topics: Background and Fundamentals of Mathematics, De Morgan’s laws,
Hausdorff Maximality Principle, Equivalence Relations, Notation
for the Logic of Mathematics and Unique Factorization Theorem.
 Proof in Mathematics An Introduction  Sets, Relations, FunctionsIvo
Duntsch and Gunther GedigaOnline  NA Pages  EnglishThis note covers the following topics: Introduction to sets, Subsets, power sets, equality of sets, Finite and
infinite sets, Set operations, De Morgan rules, distributivity, tables,
Ordered pairs, Cartesian products, Introduction to relations, Ordering
relations, Equivalence relations and Functions.
 Abstract Set TheoryThoralf
A. SkolemOnline  NA Pages  EnglishThis note covers the following topics: Ordered sets; A
theorem of Hausdorff, Axiomatic set theory; Axioms of Zermelo and Fraenkel,
The wellordering theorem, Ordinals and alephs, Set representing ordinals, The
simple infinite sequence; Development of arithmetic, The theory of Quine,
Lorenzen's operative mathematics and The possibility of set theory based on
manyvalued logic.
 Varieties of Lattices 








