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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.
Author(s): Ivo Duntsch and Gunther Gediga
NA Pages 
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 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): University of California Riverside
214 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
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): Thomas Forster
98 Pages
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.
Author(s): Norman T Hamilton
286 Pages
A Problem Course in Mathematical Logic
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA Pages
Background and Fundamentals of Mathematics
This 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.
Author(s): Edwin H.Connell
NA Pages
Proof in Mathematics An Introduction
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA Pages
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.
Author(s): Ivo Duntsch and Gunther Gediga
NA Pages
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA PagesAdvertisement
