Veröffentlicht von De Gruyter

De Gruyter Series in Logic and Its Applications

Herausgegeben von: Denis R. Hirschfeldt, Amador Martin-Pizarro, Ieke Moerdijk, Itay Neeman und Anand Pillay

ISSN: 1438-1893

Übersicht
Bände

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.

Fachgebiete

Buch 2023

Model Theory of Operator Algebras

Isaac Goldbring

Band 11 in dieser Reihe

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Continuous model theory is an extension of classical first order logic which is best suited for classes of structures which are endowed with a metric. Applications have grown considerably in the past decade. This book is dedicated to showing how the techniques of continuous model theory are used to study C*-algebras and von Neumann algebras. This book geared to researchers in both logic and functional analysis provides the first self-contained collection of articles surveying the many applications of continuous logic to operator algebras that have been obtained in the last 15 years.

DOI:: https://doi.org/10.1515/9783110768282
ISBN:: 9783110768282
ISBN:: 9783110768213
ISBN:: 9783110768336
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Fachgebiet:: Analysis
Verlag:: De Gruyter

Buch 2024

Automatic Complexity

A Computable Measure of Irregularity

Bjørn Kjos-Hanssen

Band 12 in dieser Reihe

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Automatic complexity is a computable and visual form of Kolmogorov complexity. Introduced by Shallit and Wang in 2001, it replaces Turing machines by finite automata, and has connections to normalized information distance, logical depth, and linear diophantine equations. Automatic Complexity is the first book on the subject and includes exercises with solutions written for the proof assistant Lean, computer programs to calculate automatic complexity, and many open problems.

DOI:: https://doi.org/10.1515/9783110774870
ISBN:: 9783110774870
ISBN:: 9783110774818
ISBN:: 9783110774900
Fachgebiet:: Informatik
Fachgebiet:: Theoretische Informatik
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Fachgebiet:: Diskrete Mathematik
Fachgebiet:: Mathematik, Allgemeines
Verlag:: De Gruyter

Buch 2022

The Ultrapower Axiom

Gabriel Goldberg

Band 10 in dieser Reihe

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The book is about strong axioms of infi nity in set theory (also known as large cardinal axioms), and the ongoing search for natural models of these axioms. Assuming the Ultrapower Axiom, a combinatorial principle conjectured to hold in all such natural models, we solve various classical problems in set theory (for example, the Generalized Continuum Hypothesis) and uncover a theory of large cardinals that is much clearer than the one that can be developed using only the standard axioms.

DOI:: https://doi.org/10.1515/9783110719734
ISBN:: 9783110719734
ISBN:: 9783110719796
ISBN:: 9783110719697
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 2019

Ordinal Computability

An Introduction to Infinitary Machines

Merlin Carl

Band 9 in dieser Reihe

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Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.

DOI:: https://doi.org/10.1515/9783110496154
ISBN:: 9783110496154
ISBN:: 9783110495621
ISBN:: 9783110492910
Fachgebiet:: Informatik
Fachgebiet:: Theoretische Informatik
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Fachgebiet:: Diskrete Mathematik
Verlag:: De Gruyter

Buch 2015

Recursion Theory

Computational Aspects of Definability

Chi Tat Chong, Liang Yu

Band 8 in dieser Reihe

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This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory.
The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.

DOI:: https://doi.org/10.1515/9783110275643
ISBN:: 9783110275551
ISBN:: 9783110275643
ISBN:: 9783110381290
Fachgebiet:: Informatik
Fachgebiet:: Theoretische Informatik
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 2004

The Determinacy of Long Games

Itay Neeman

Band 7 in dieser Reihe

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In diesem Band entwickelt und verwendet der Autor Verfahren, um - ausgehend von großen Kardinalzahlen - die Determiniertheit von definierbaren Spielen mit abzählbarer Länge auf natürlichen Zahlen nachzuweisen. Die Determiniertheit ist letztlich abgeleitet von Iterationsstrategien, die Spiele auf natürlichen Zahlen mit den spezifischen iterativen Spielen verbinden, die bei der Untersuchung großer Kardinalzahlen aufkommen.

DOI:: https://doi.org/10.1515/9783110200065
ISBN:: 978-3-11-018341-2
ISBN:: 978-3-11-020006-5
Fachgebiet:: Informatik
Fachgebiet:: Theoretische Informatik
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 2004

One Hundred Years of Russell´s Paradox

Mathematics, Logic, Philosophy

Godehard Link, John L. Bell, Ulrich Blau, Andrea Cantini, Solomon Feferman, Hartry Field, Harvey M. Friedman, Sy-David Friedman, Nicholas Griffin, Kai Hauser, Allen P. Hazen, Geoffrey Hellman, Tobias Hürter, Andrew D. Irvine, Gerhard Jäger, Gregory Landini, Shaughan Lavine, Bernard Linsky, David Charles McCarty, Vann McGee, Jan Mycielsky, Karl-Georg Niebergall, Volker Peckhaus, Dieter Probst, Michael Rathjen, Francisco Rodriguez-Consuegra, Philippe de Rouilhan, Peter Schuster, Helmut Schwichtenberg, Holger Sturm, Robert S. D. Thomas, Albert Visser, Kai F. Wehmeier, W. Hugh Woodin

Band 6 in dieser Reihe

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Die in diesem Band zusammengefassten Beiträge stellen die wesentlichen Forschungsergebnisse der internationalen Münchner Konferenz "100 Jahre Russell-Paradoxon" im Jahr 2001 dar, auf der an die Entdeckung des berühmten Russell Paradoxons vor 100 Jahren erinnert wurde. Die 31 Beiträge und der Einführungsessay des Herausgebers wurden alle - bis auf zwei Ausnahmen - ursprünglich für diesen Band verfasst.

DOI:: https://doi.org/10.1515/9783110199680
ISBN:: 978-3-11-017438-0
ISBN:: 978-3-11-019968-0
Fachgebiet:: Mathematik
Fachgebiet:: Geschichte und Philosophie
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 2002

Inner Models and Large Cardinals

Martin Zeman

Band 5 in dieser Reihe

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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.

DOI:: https://doi.org/10.1515/9783110857818
ISBN:: 978-3-11-016368-1
ISBN:: 978-3-11-085781-8
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 2001

Aspects of Complexity

Minicourses in Algorithmics, Complexity and Computational Algebra. Mathematics Workshop, Kaikoura, January 7-15, 2000

Rod Downey, Denis R. Hirschfeldt

Band 4 in dieser Reihe

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The book contains 8 detailed expositions of the lectures given at the Kaikoura 2000 Workshop on Computability, Complexity, and Computational Algebra.

Topics covered include basic models and questions of complexity theory, the Blum-Shub-Smale model of computation, probability theory applied to algorithmics (randomized alogrithms), parametric complexity, Kolmogorov complexity of finite strings, computational group theory, counting problems, and canonical models of ZFC providing a solution to continuum hypothesis.

The text addresses students in computer science or mathematics, and professionals in these areas who seek a complete, but gentle introduction to a wide range of techniques, concepts, and research horizons in the area of computational complexity in a broad sense.

DOI:: https://doi.org/10.1515/9783110889178
ISBN:: 978-3-11-016810-5
ISBN:: 978-3-11-088917-8
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 2000

Fine Structure and Class Forcing

Sy D. Friedman

Band 3 in dieser Reihe

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DOI:: https://doi.org/10.1515/9783110809114
ISBN:: 978-3-11-016777-1
ISBN:: 978-3-11-080911-4
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 1999

Recursion Theory and Complexity

Proceedings of the Kazan '97 Workshop, Kazan, Russia, July 14–19, 1997

Marat M. Arslanov, Steffen Lempp

Band 2 in dieser Reihe

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DOI:: https://doi.org/10.1515/9783110807486
ISBN:: 978-3-11-016587-6
ISBN:: 978-3-11-080748-6
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 1999

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

W. Hugh Woodin

Band 1 in dieser Reihe

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DOI:: https://doi.org/10.1515/9783110804737
ISBN:: 9783110157086
ISBN:: 9783110804737
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter

Buch 2010

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

W. Hugh Woodin

Band 1 in dieser Reihe

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The starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the non-stationary ideal on ω₁; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universal-existential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method.

This monograph is directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of Ω-logic and related matters.

DOI:: https://doi.org/10.1515/9783110213171
ISBN:: 978-3-11-019702-0
ISBN:: 978-3-11-021317-1
Fachgebiet:: Mathematik
Fachgebiet:: Logik und Mengentheorie
Verlag:: De Gruyter