Inner Models and Large Cardinals / Edition 1

by Martin Zeman

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.

Product Details

ISBN-13:	9783110163681
Publisher:	De Gruyter
Publication date:	12/12/2001
Series:	De Gruyter Series in Logic and Its Applications , #5
Edition description:	Reprint 2011
Pages:	380
Product dimensions:	6.14(w) x 9.21(h) x 0.88(d)
Age Range:	18 Years

About the Author

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

Table of Contents

Preface · Fine Structure · Extenders and Coherent Structures · Fine Ultrapowers · Mice and Iterability · Solidity and Condensation · Extender Models · The Core Model · One Strong Cardinal · Overlapping Extenders · Bibliography · Index

Editorial Reviews

"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

"This elegant volume provides a systematic introduction to the theory of fine structural inner models of set theory. […] The author can fairly claim to have systematized the theory through to strong cardinals […]." Mathematical Reviews

"The book is a well-written and self-contained introduction to the theory of fine structural inner models, an area of set theory concerned with questions about models of set theory. […] The author gives an introduction to the techniques of this theory; so the book can serve as a textbook even for graduate students." Zentralblatt für Mathematik

From the Publisher

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)