The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.
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.
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
Professor Martin Zeman, Institut für formale Logik, University Vienna, Vienna, Austria.
"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
