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Inner Models and Large Cardinals / Edition 1

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Overview

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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Editorial Reviews

From the Publisher
"Insgesamt ist Zeman ein ausgezeichnetes Lehrbuch über Kernmodelltheorie gelungen. Es ist sehr gut zum Selbststudium geeignet."H.-D. Donder, Jahresbericht der Deutschen Mathematiker-Vereinigung 106, 3-2004
From The Critics
A graduate textbook or tutorial for mathematics professionals introducing the theory of fine structural inner models. It begins by detailing the general fine structure theory of acceptable structures, then presents the full core model theory for measures of order 0 and instructions for generalizing it for models that can contain up to one strong cardinal, and concludes with the theory of Jensen extender models that are beyond one strong cardinal. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Meet the Author

Professor Martin Zeman, Institut für formale Logik, University Vienna, Vienna, Austria.
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Table of Contents

Preface
1 Fine Structure 1
2 Extenders and Coherent Structures 47
3 Fine Ultrapowers 71
4 Mice and Iterability 109
5 Solidity and Condensation 146
6 Extender Models 175
7 The Core Model 212
8 One Strong Cardinal 251
9 Overlapping Extenders 280
Bibliography 359
Index 365
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