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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
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 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
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
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
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
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.
Author(s): Thoralf A. Skolem
NA Pages
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Author(s): NA
NA PagesAdvertisement
