Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
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 
An Introduction to Set Theory and Topology
These notes are an introduction to set theory and topology. Topics covered includes: Sets, Pseudometric Spaces, Topological Spaces, Completeness and Compactness, Connected Spaces, Products and Quotients, Separation Axioms, Ordered Sets, Ordinals and Transfinite Methods, Convergence and Compactifications.
Author(s): Ronald C. Freiwald, Washington University in St. Louis
459 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
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
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.
Author(s): Toby Meadows
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
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
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
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
