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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): Jean-louis Krivine
65 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
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
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
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): Glynn Winskel
141 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
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
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA PagesAdvertisement
