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.
This note is an
introduction to the Zermelo–Fraenkel set theory with Choice (ZFC). Topics
covered includes: The axioms of set theory , Ordinal and cardinal arithmetic,
The axiom of foundation, Relativisation, absoluteness, and reflection, Ordinal
definable sets and inner models of set theory, The constructible universe L
Cohen's method of forcing, Independence of the axiom of choice and the continuum
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.
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: 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