set theory
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Description
Book Introduction
Thoroughly revised, expanded, and reorganized for use as a basic textbook in mathematics curricula, Set Theory, Third Edition covers fundamental concepts such as relations, functions, sequences; finite, countable, and uncountable sets; cardinal and ordinal numbers, in nine chapters suitable for one semester.
We also added five additional chapters, integrated them into a separate chapter on real numbers to allow for flexible curriculum design, provided a final section with practice problems with hints of varying difficulty, and provided various applications of the axiom of choice, including normal forms and Goodstein sequences.
We add important recent concepts including filters, superfilters, closed and unbounded sets and normal sets, partitions, and delve into combinatorial principles such as Diamond and Martin's axioms.
We discuss large cardinal numbers, take a renewed interest in measurable cardinal numbers, study the cardinal sets in detail, and delve into non-cardinal sets, a topic related to computer science, mathematics, linguistics, and nonstandard analysis.
We introduce the partitioning method, study trees, develop their relationship to the Suslin problem, prove Silver's theorem, and so on...
It covers a lot of content.
We also added five additional chapters, integrated them into a separate chapter on real numbers to allow for flexible curriculum design, provided a final section with practice problems with hints of varying difficulty, and provided various applications of the axiom of choice, including normal forms and Goodstein sequences.
We add important recent concepts including filters, superfilters, closed and unbounded sets and normal sets, partitions, and delve into combinatorial principles such as Diamond and Martin's axioms.
We discuss large cardinal numbers, take a renewed interest in measurable cardinal numbers, study the cardinal sets in detail, and delve into non-cardinal sets, a topic related to computer science, mathematics, linguistics, and nonstandard analysis.
We introduce the partitioning method, study trees, develop their relationship to the Suslin problem, prove Silver's theorem, and so on...
It covers a lot of content.
- You can preview some of the book's contents.
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index
Chapter 1: Set
1.
Set Overview
2.
attribute
3.
axiom
4.
Basic operations on sets
Chapter 2: Relations, Functions, and Order
1.
ordered pairs
2.
relationship
3.
function
4.
Equivalence and division
5.
order
Chapter 3: Natural Numbers
1.
Natural Numbers Overview
2.
Properties of natural numbers
3.
Circular theorem
4.
Natural number operations
5.
Operation and Structure
Chapter 4: Finite, Countable, and Uncountable Sets
1.
Cardinality of a set
2.
finite set
3.
countable set
4.
linear order
5.
Completely linear order
6.
uncountable sets
Chapter 5: The Riders
1.
Radix operation
2.
cardinal points of the continuum
Chapter 6: Ordinal Numbers
1.
ordered-sorted set
2.
Ordinal number
3.
Substitution axiom
4.
Transcendental induction and circulation
5.
Ordinal number operations
6.
regular form
Chapter 7: Aleph
1.
Initial ordinal number
2.
Aleph addition and multiplication
Chapter 8: The Axiom of Choice
1.
The axiom of choice and its equivalents
2.
Application of the axiom of choice
Chapter 9: Arithmetic of Radixes
1.
Infinite sum and product of cardinal numbers
2.
Regular riders and special riders
3.
exponent of the base
Chapter 10: The Set of Real Numbers
1.
Integers and rational numbers
2.
mistake
3.
Phase of the solid line
4.
set of real numbers
5.
Borel set
Chapter 11: Filters, Superfilters
1.
Filter, Ideal
2.
Super filter
3.
Closed and unbounded sets and normal sets
4.
Silver Cleanup
Chapter 12: Combinatorial Set Theory
1.
Ramsey's theorem
2.
Partitioning Calculus for Uncountable Cardinal Numbers
3.
tree
4.
Suslin hypothesis
5.
Combination principle
Chapter 13: The Big Horseman
1.
Measurement problem
2.
big rider
Chapter 14: The Normality Axiom
1.
Jeongcho relationship
2.
New Year's gathering
3.
A set that is not the beginning
Chapter 15: Axiomatic Set Theory
1.
Zermelo-Fraenkel set theory with the axiom of choice
2.
Consistency and independence
3.
The Universe of Set Theory
1.
Set Overview
2.
attribute
3.
axiom
4.
Basic operations on sets
Chapter 2: Relations, Functions, and Order
1.
ordered pairs
2.
relationship
3.
function
4.
Equivalence and division
5.
order
Chapter 3: Natural Numbers
1.
Natural Numbers Overview
2.
Properties of natural numbers
3.
Circular theorem
4.
Natural number operations
5.
Operation and Structure
Chapter 4: Finite, Countable, and Uncountable Sets
1.
Cardinality of a set
2.
finite set
3.
countable set
4.
linear order
5.
Completely linear order
6.
uncountable sets
Chapter 5: The Riders
1.
Radix operation
2.
cardinal points of the continuum
Chapter 6: Ordinal Numbers
1.
ordered-sorted set
2.
Ordinal number
3.
Substitution axiom
4.
Transcendental induction and circulation
5.
Ordinal number operations
6.
regular form
Chapter 7: Aleph
1.
Initial ordinal number
2.
Aleph addition and multiplication
Chapter 8: The Axiom of Choice
1.
The axiom of choice and its equivalents
2.
Application of the axiom of choice
Chapter 9: Arithmetic of Radixes
1.
Infinite sum and product of cardinal numbers
2.
Regular riders and special riders
3.
exponent of the base
Chapter 10: The Set of Real Numbers
1.
Integers and rational numbers
2.
mistake
3.
Phase of the solid line
4.
set of real numbers
5.
Borel set
Chapter 11: Filters, Superfilters
1.
Filter, Ideal
2.
Super filter
3.
Closed and unbounded sets and normal sets
4.
Silver Cleanup
Chapter 12: Combinatorial Set Theory
1.
Ramsey's theorem
2.
Partitioning Calculus for Uncountable Cardinal Numbers
3.
tree
4.
Suslin hypothesis
5.
Combination principle
Chapter 13: The Big Horseman
1.
Measurement problem
2.
big rider
Chapter 14: The Normality Axiom
1.
Jeongcho relationship
2.
New Year's gathering
3.
A set that is not the beginning
Chapter 15: Axiomatic Set Theory
1.
Zermelo-Fraenkel set theory with the axiom of choice
2.
Consistency and independence
3.
The Universe of Set Theory
Publisher's Review
“This book is very suitable as a textbook for fourth-year undergraduate or first-year graduate students.
There is enough material for professors with different perspectives to teach a semester's worth of courses.
“The chapter on the axiom of choice is particularly helpful.” - Mathematical Reviews
There is enough material for professors with different perspectives to teach a semester's worth of courses.
“The chapter on the axiom of choice is particularly helpful.” - Mathematical Reviews
GOODS SPECIFICS
- Date of issue: July 1, 2025
- Page count, weight, size: 384 pages | 188*257*30mm
- ISBN13: 9791160732733
- ISBN10: 1160732736
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