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.
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.
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.
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.
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: 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.
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.