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Set Theory Books

Set Theory Books

There are many online resources where you can find free Set Theory books to download in PDF format, including online textbooks, ebooks, lecture notes, and more, covering basic, beginner, and advanced concepts for those looking for an introduction to the subject or a deeper understanding of it.

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):

s 65Pages

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, Zornís Lemma, Ramseyís Theorem, Loīsís Theorem, Cumulative Hierarchy, Relativization, Measurable Cardinals, Godelís Constructible Universe, Banach-Tarski Paradox.

Author(s):

s 60Pages

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):

s 214Pages

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):

s 105Pages

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):

s 91Pages

Set Theory Some Basics And A Glimpse Of Some Advanced Techniques

Goal 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.

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s 91Pages

Lectures On Set Theory

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

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s 602Pages

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):

s 119Pages

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, Well-founded induction, Inductively-defined classes and Fraenkel-Mostowski sets.

Author(s):

s 141Pages

The Axioms of Set Theory

This 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.

Author(s):

s 98Pages

Set theory and the structure of arithmetic

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.

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s 286Pages

A Problem Course in Mathematical Logic

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Author(s):

s NAPages

Background and Fundamentals of Mathematics

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.

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s NAPages

Proof in Mathematics An Introduction

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s NAPages

Sets, Relations, Functions

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.

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s NAPages

Abstract Set Theory

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.

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s NAPages

Varieties of Lattices

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Author(s):

s NAPages