《集合論導論（第2版）》是2016年1月1日世界圖書出版公司出版的圖書，作者是Robert、L.Vaught 。
基本介紹
- 中文名：集合論導論（第2版）
- 作者：Robert、L.Vaught
- 出版時間：2016年01月01日
- 出版社：世界圖書出版公司
- ISBN：9787519200169
內容簡介,目錄,
內容簡介
《集合論導論（第2版 英文版）》是一本關於集合論的本科生教材，內容涉及：集合及其關係運算；基數和有限集；數系；基數；序及序型；公理集合論；良序、基數及序數；正則公理；邏輯和形式理論；獨立性證明；基數和序等。
目錄
Preface
Introduction
1．Sets and Relations and Operations among them
1．Set algebra and the set-builder
2．Russell's paradox
3．Infinite unions and intersections
4．Ordered couples and Cartesian products
5．Relations and functions
6．Sets of sets， power set， arbitrary Cartesian product
7．Structures
8．Partial orders and orders
2．Cardinal Numbers and Finite Sets
1．Cardinal numbers， +， and ≤
2．Natural numbers and finite sets
3．Multiplication and exponentiation
4．Definition by induction
5．Axiom of infinity， Peano axioms， Dedekind infinite sets
3．The Number Systems
1．Introductory remarks
2．Construction and characterization up to isomorphism of the integers， rationals， and reals
4．More on Cardinal Numbers
1．The Cantor-Bernstein Theorem
2．Infinite sums and products of cardinals
3．Different kinds of infinity
4．N0， 2N0， and 22N0- the simplest infinite cardinals
5．Orders and Order Types
1．Ordered sums and products
2．Order types
6．Axiomatic Set Theory
1．A formalized language
2．The axioms of set theory
3．On Chapter 1
4．On Chapters 2-5
7．Well-orderings， Cardinals， and Ordinals
1．Well-orders
2．Von Neumann ordinals
3．The well-ordering theorem
4．Defining A and TpA
5．Easy consequences for cardinals of the Well-ordering Principle
6．A harder consequence and its corollaries
7．The Continuum hypothesis
8．The Axiom of Regularity
1．Partial universes and the axiom of regularity
2．Consequences of regularity
3．Avoiding replacement
9．Logic and Formalized Theories
1．Language and grammar
2．Truth and tables
3．Formal proofs
4．Substitution for predicate symbols and relativization
5．Three forms of ZFC
10．Independence Proofs
1．Relativization of axioms to partial universes．Consistency of adding Reg．
2．Three other consistency results
3．Informal note on the set theories NB and M
11．More on Cardinals and Ordinals
1．Character of cofinality
2．More on ordinal arithmetic
Appendix
Proofs of some results in Chapter 9
Bibliography
Other References
Recommendations for more advanced reading
Index
Solutions to Selected Problems
