Set Theory and Forcing Lecture Notes by Jean louis Krivine
Set Theory and Forcing Lecture Notes by Jean louis Krivine
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.
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
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.
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.
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.
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.
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.
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.
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.
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.