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

Set Theory Books
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An Introduction To Set Theory

PDF | 119 Pages | English
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.

 
Set Theory for Computer Science

PDF | 141 Pages | English
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, Well-founded induction, Inductively-defined classes and Fraenkel-Mostowski sets.

 
Set theory and the structure of arithmetic

Online | 286 Pages | English
The 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 Mathematics

Online | NA Pages | English
This note covers the following topics: Background and Fundamentals of Mathematics, De Morganís laws, Hausdorff Maximality Principle, Equivalence Relations, Notation for the Logic of Mathematics and Unique Factorization Theorem.

 
Proof in Mathematics An Introduction
Sets, Relations, Functions

Online | NA Pages | English
This 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 Theory

Online | NA Pages | English
This note covers the following topics: Ordered sets; A theorem of Hausdorff, Axiomatic set theory; Axioms of Zermelo and Fraenkel, The well-ordering 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 many-valued logic.

 
Varieties of Lattices
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