Inner Models and Large Cardinals

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Walter de Gruyter, 2002 - Mathematics - 369 pages
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This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large cardinal properties of the set theoretic universe.

The monograph contains a detailed presentation of general fine structure theory as well as a modern approach to the construction of small core models, namely those models containing at most one strong cardinal, together with some of their applications. The final part of the book is devoted to a new approach encompassing large inner models which admit many Woodin cardinals.

The exposition is self-contained and does not assume any special prerequisities, which should make the text comprehensible not only to specialists but also to advanced students in Mathematical Logic and Set Theory.

 

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Contents

Fine Structure
1
Extenders and Coherent Structures
47
Fine Ultrapowers
71
Mice and Iterability
109
Solidity and Condensation
146
Extender Models
175
The Core Model
212
One Strong Cardinal
251
Overlapping Extenders
280
Bibliography
359
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Popular passages

Page 360 - JENSEN, The fine structure of the constructible hierarchy, Ann. of Math. Logic 4 (1972), 229-308.
Page 361 - Fine structure and iteration trees, Lecture Notes in Logic 3, Springer, Berlin 1994.

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About the author (2002)

Professor Martin Zeman, Institut f r formale Logik, University Vienna, Vienna, Austria. 

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