This note will be permanently deleted and cannot be recovered. Are you sure?
Are you sure you wish to share this note?
Sorry, you can only share notes on selected books with the reading experience feature.
Please choose the Show Notes option before creating a new note.
By John P. Mayberry
Publisher: Cambridge University Press
Print Publication Year:2001
Online Publication Date:March 2012
Online ISBN:9781139087124
Hardback ISBN:9780521770347
Paperback ISBN:9780521172714
Book DOI: http://dx.doi.org/10.1017/CBO9781139087124
Subjects: Logic, categories and Sets , Philosophy: general interest
This unified approach to the foundations of mathematics in the theory of sets covers both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of "natural number" and "set". The book contains an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, and the analysis of proof by induction and definition by recursion. The book should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.
Reviews:
pp. i-vi
pp. vii-ix
pp. x-xx
Part One - Preliminaries: Read PDF
pp. 1-2
1 - The Idea of Foundations for Mathematics: Read PDF
pp. 3-16
2 - Simple Arithmetic: Read PDF
pp. 17-64
Part Two - Basic Set Theory: Read PDF
pp. 65-66
3 - Semantics, Ontology, and Logic: Read PDF
pp. 67-110
4 - The Principal Axioms and Definitions of Set Theory: Read PDF
pp. 111-150
Part Three - Cantorian Set Theory: Read PDF
pp. 151-152
5 - Cantorian Finitism: Read PDF
pp. 153-190
6 - The Axiomatic Method: Read PDF
pp. 191-236
7 - Axiomatic Set Theory: Read PDF
pp. 237-258
Part Four - Euclidean Set Theory: Read PDF
pp. 259-260
8 - Euclidean Finitism: Read PDF
pp. 261-299
9 - The Euclidean Theory of Cardinality: Read PDF
pp. 300-324
10 - The Euclidean Theory of Simply Infinite Systems: Read PDF
pp. 325-368
11 - Euclidean Set Theory from the Cantorian Standpoint: Read PDF
pp. 369-380
pp. 381-395
Appendix 1 - Conceptual Notation: Read PDF
pp. 396-410
Appendix 2 - The Rank of a Set: Read PDF
pp. 411-414
pp. 415-420
pp. 421-424