The Higher Infinite

Large Cardinals in Set Theory from Their Beginnings

Author: Akihiro Kanamori

Publisher: Springer Science & Business Media

ISBN: 3540888667

Category: Mathematics

Page: 538

View: 620

Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.

Set Theory and Its Applications

Annual Boise Extravaganza in Set Theory, Boise, Idaho, 1995-2010

Author: Liljana Babinkostova

Publisher: American Mathematical Soc.

ISBN: 0821848127

Category: Mathematics

Page: 330

View: 643

This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.

Logic Colloquium 2007

Author: Françoise Delon,Ulrich Kohlenbach,Penelope Maddy,Frank Stephan

Publisher: Cambridge University Press

ISBN: 1139488937

Category: Mathematics

Page: 267

View: 7575

The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay's conjecture, and on automatic structures. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.

Combinatorial Set Theory

With a Gentle Introduction to Forcing

Author: Lorenz J. Halbeisen

Publisher: Springer Science & Business Media

ISBN: 9781447121732

Category: Mathematics

Page: 456

View: 4585

This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

The Stationary Tower

Notes on a Course by W. Hugh Woodin

Author: Paul Bradley Larson,W. Hugh Woodin,E B Dynkin

Publisher: American Mathematical Soc.

ISBN: 0821836048

Category: Mathematics

Page: 132

View: 943

The stationary tower is an important method in modern set theory invented by Hugh Woodin in the 1980s. It is a means of constructing generic elementary embeddings and can be applied to produce a variety of useful forcing effects. Hugh Woodin is a leading figure in modern set theory, having made many deep and lasting contributions to the field, in particular to descriptive set theory and large cardinals. This book is the first detailed treatment of his method of the stationary tower that is generally accessible to graduate students in mathematical logic. It should become the standard reference on the stationary tower and its applications to descriptive set theory. The book is suitable for a graduate course that assumes some familiarity with forcing, constructibility, and ultrapowers.

Foundations of the Formal Sciences V

Infinite Games

Author: Stefan Bold,B Loewe,T Rasch

Publisher: N.A

ISBN: 9781904987758

Category: Computers

Page: 351

View: 835

Infinity can feature in games in various forms: we can play games of infinite length, with infinitely many players, or allow for infinitely many moves or strategies. Games of infinite length have been thoroughly investigated by mathematicians and have played a central role in mathematical logic. However, their applications go far beyond mathematics: they feature prominently in theoretical computer science, philosophical Gedankenexperiments, as limit cases in economical applications, and in many other applications. The conference Foundations of the Formal Sciences V focused on games of infinite length, but was very opn to include other notions of infinity in games as well.