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Foundations Introduction to Set Theory by Hrbacek and Jech

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  1. Jan 28, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Preface
    [*] Sets
    [LIST]
    [*] Introduction to Sets
    [*] Properties
    [*] The Axioms
    [*] Elementary Operations on gets
    [/LIST]
    [*] Relations, Functions, and Orderings
    [LIST]
    [*] Ordered Pairs
    [*] Relations
    [*] Functions
    [*] Equivalences and Partitions
    [*] Orderings
    [/LIST]
    [*] Natural Numbers
    [LIST]
    [*] Introduction to Natural Numbers
    [*] Properties of Natural Numbers
    [*] The Recursion Theorem
    [*] Arithmetic of Natural Numbers
    [*] Operations and Structures
    [/LIST]
    [*] Finite, Countable, and Uncountable Sets
    [LIST]
    [*] Cardinality of gets
    [*] Finite Sets
    [*] Countable gets
    [*] Linear Orderings
    [*] Complete Linear Orderings
    [*] Uncountable gets
    [/LIST]
    [*] Cardinal Numbers
    [LIST]
    [*] Cardinal Arithmetic
    [*] The Cardinality of the Continuum
    [/LIST]
    [*] Ordinal Numbers
    [LIST]
    [*] Well-Ordered Sets
    [*] Ordinal Numbers
    [*] The Axiom of Replacement
    [*] Transfinite Induction and Recursion
    [*] Ordinal Arithmetic
    [*] The Normal Form
    [/LIST]
    [*] Alephs
    [LIST]
    [*] Initial Ordinals
    [*] Addition and Multiplication of Alephs
    [/LIST]
    [*] The Axiom of Choice
    [LIST]
    [*] The Axiom of Choice and its Equivalents
    [*] The Use of the Axiom of Choice in Mathematics
    [/LIST]
    [*] Arithmetic of Cardinal Numbers
    [LIST]
    [*] Infinite Sums and Products of Cardinal Numbers
    [*] Regular and Singular Cardinals
    [*] Exponentiation of Cardinals
    [/LIST]
    [*] Sets of Real Numbers
    [LIST]
    [*] Integers and Rational Numbers
    [*] Real Numbers
    [*] Topology of the Real Line
    [*] Sets of Real Numbers
    [*] Borel Sets
    [/LIST]
    [*] Filters and Ultrafilters
    [LIST]
    [*] Filters and Ideals
    [*] Ultrafilters
    [*] Closed Unbounded and Stationary Sets
    [*] Silver's Theorem
    [/LIST]
    [*] Comblnatorial Set Theory
    [LIST]
    [*] Ramsey's Theorems
    [*] Partition Calculus for Uncountable Cardinals
    [*] Trees
    [*] Suslin's Problem
    [*] Combinatorial Principles
    [/LIST]
    [*] Large Cardinals
    [LIST]
    [*] The Measure Problem
    [*] Large Cardinals
    [/LIST]
    [*] The Axiom of Foundation
    [LIST]
    [*] Well-Founded Relations
    [*] Well-Founded Set
    [*] Non-Well-Founded Sets
    [/LIST]
    [*] The Axiomatic Set Theory
    [LIST]
    [*] The Zermelo-Praenkel Set Theory With Choice
    [*] Consistency and Independence
    [*] The Universe of Set Theory
    [/LIST]
    [*] Bibliography
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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