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Inner Models and Large Cardinals : Travaux de la Faculte de Theologie Protestante de Strasbourg - Martin Zeman

Inner Models and Large Cardinals

Travaux de la Faculte de Theologie Protestante de Strasbourg

Hardcover Published: 1st January 2002
ISBN: 9783110163681
Number Of Pages: 380
For Ages: 22+ years old

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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.

"Insgesamt ist Zeman ein ausgezeichnetes Lehrbuch uber Kernmodelltheorie gelungen. Es ist sehr gut zum Selbststudium geeignet."H.-D. Donder, Jahresbericht der Deutschen Mathematiker-Vereinigung 106, 3-2004

Prefacep. v
Fine Structurep. 1
Acceptable J-Structuresp. 1
The [Sigma subscript 1]-Projectump. 6
Downward Extension of Embeddings Lemmatap. 8
Upward Extension of Embeddings Lemmap. 12
Iterated Projectap. 18
[Sigma]*-Relationsp. 20
[Sigma superscript (n) subscript l]-Embeddingsp. 23
Substitution and Good Functionsp. 26
Standard Parametersp. 33
Two Applications to Lp. 36
More on Downward Extensions of Embeddingsp. 38
Witnesses and Solidityp. 41
Notesp. 45
Extenders and Coherent Structuresp. 47
Extendersp. 47
The Hypermeasure Representation of Extendersp. 54
Amenabilityp. 56
Coherent Structuresp. 58
Extendibilityp. 61
Strong Cardinalsp. 68
Notesp. 70
Fine Ultrapowersp. 71
The *-Ultrapower Constructionp. 71
Some Special Preservation Propertiesp. 82
When F Is Close to Mp. 85
Extendibilityp. 89
k-Ultrapowersp. 93
Pseudoultrapowersp. 96
Notesp. 108
Mice and Iterabilityp. 109
Premicep. 109
Iterationsp. 114
Copying and the Dodd--Jensen Lemmap. 119
Comparison Processp. 127
Some Iterability Criteriap. 131
Bicephalip. 142
Notesp. 145
Solidity and Condensationp. 146
Cores and Coiterationsp. 146
The Solidity Theoremp. 150
Consequences of Solidityp. 155
The Canonical Ordering of Micep. 160
Condensation Lemmap. 163
Upwards Extensions to Premicep. 167
Notesp. 174
Extender Modelsp. 175
Extender Models and Iterationsp. 175
The Canonical Ordering of Weaselsp. 178
Universalityp. 183
The Model K[superscript c]p. 186
0[superscript ++]p. 198
Weak Coveringp. 203
Notesp. 211
The Core Modelp. 212
Inductive Definition of Kp. 212
Steel's Definition of Kp. 214
The Existence of Kp. 218
Embeddings of K and Generic Absolutenessp. 230
Weak Covering for Kp. 235
Notesp. 249
One Strong Cardinalp. 251
Premicep. 251
Properties of Micep. 258
Extender Models up to One Strong Cardinalp. 269
Notesp. 279
Overlapping Extendersp. 280
Premice and Iteration Treesp. 281
Copying and the Dodd--Jensen Propertyp. 299
Solidity and Condensationp. 318
Uniqueness of Well-Founded Branchesp. 345
Towards the Ultimate Model K[superscript c]p. 355
Notesp. 358
Bibliographyp. 359
Indexp. 365
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9783110163681
ISBN-10: 3110163683
Series: Travaux de la Faculte de Theologie Protestante de Strasbourg
Audience: Professional
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 380
Published: 1st January 2002
Country of Publication: DE
Dimensions (cm): 24.54 x 18.09  x 2.52
Weight (kg): 0.76