TY  - BOOK
AU  - Moschovakis,Yiannis
ED  - SpringerLink (Online service)
TI  - Notes on Set Theory
T2  - Undergraduate Texts in Mathematics,
SN  - 9780387316093
U1  - 511.3 23
PY  - 2006///
CY  - New York, NY
PB  - Springer New York
KW  - MATHEMATICS
KW  - COMPUTER SCIENCE
KW  - LOGIC, SYMBOLIC AND MATHEMATICAL
KW  - MATHEMATICAL LOGIC AND FOUNDATIONS
KW  - MATHEMATICAL LOGIC AND FORMAL LANGUAGES
N1  - Equinumerosity -- Paradoxes and Axioms -- Are Sets All There is? -- The Natural Numbers -- Fixed Points -- Well Ordered Sets -- Choices -- Choice's Consequences -- Baire Space -- Replacement and Other Axioms -- Ordinal Numbers
N2  - The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects of the subject: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author added solutions to the exercises, and rearranged and reworked the text in several places to improve the presentation. The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy
UR  - http://dx.doi.org/10.1007/0-387-31609-4
ER  -