TY  - BOOK
AU  - Schindler,Ralf
TI  - Set theory : : exploring independence and truth 
T2  - Universitext
SN  - 9783319067247
U1  - 511.322 23
PY  - 2014///
CY  - New York
PB  - Springer
KW  - Set theory.
KW  - Symbolic and mathematical Logic
KW  - Mathematics.
N1  - Includes bibliographical references and index; 1. Naive set theory --
2. Axiomatic set theory --
3. Ordinals --
4. Cardinals --
5. Constructibility --
6. Forcing --
7. Descriptive set theory --
8. Solovay's model --
9. The Raisonnier filter --
10. Measurable cardinals --
11. 0[superscript]# and Jensen's covering lemma --
12. Analytic and full determinacy --
13. Projective determinacy--

References--
Index
N2  - This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing, and descriptive set theory. The following topics are covered: - Forcing and constructability - The Solovay-Shelah Theorem i.e. the equiconsistency of 'every set of reals is Lebesgue measurable' with one inaccessible cardinal - Fine structure theory and a modern approach to sharps - Jensen's Covering Lemma - The equivalence of analytic determinacy with sharps - The theory of extenders and iteration trees - A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers
ER  -