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This series serves researchers, teachers and students in the field of symbolic logic, broadly interpreted. The aim of the series is to bring publications to the logic community with the least possible delay and to provide rapid dissemination of the latest research. Scientific quality is the overriding criterion by which submissions are evaluated. More information, including a list of the books in the series, can be found at https://aslonline.org/books/.

  • General Editors: Paul Larson, Miami University
  • Editorial Boards: Denis Hirschfeldt, University of Chicago, Leon Horsten, Universität Konstanz, Germany, Paulo Oliva, Queen Mary University of London, Martin Otto, Technische Universität, Darmstadt, Germany, Maryanthe Malliaris, University of Chicago, Andrew Marks, University of California, Berkeley

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56 results in Lecture Notes in Logic

Page 1 of 3

The Largest Suslin Axiom
  • Grigor Sargsyan, Nam Trang
  • Published online:
    07 June 2024
    Print publication:
    27 June 2024
  • Developing the theory up to the current state-of-the art, this book studies the minimal model of the Largest Suslin Axiom (LSA), which is one of the most important determinacy axioms and features prominently in Hugh Woodin's foundational framework known as the Ultimate L. The authors establish the consistency of LSA relative to large cardinals and develop methods for building models of LSA from other foundational frameworks such as Forcing Axioms. The book significantly advances the Core Model Induction method, which is the most successful method for building canonical inner models from various hypotheses. Also featured is a proof of the Mouse Set Conjecture in the minimal model of the LSA. It will be indispensable for graduate students as well as researchers in mathematics and philosophy of mathematics who are interested in set theory and in particular, in descriptive inner model theory.

A Theory of Truth
  • Yannis Stephanou
  • Published online:
    07 October 2023
    Print publication:
    12 October 2023
  • How should we treat the liar and kindred paradoxes? A Theory of Truth argues that we should diverge from classical logic, and presents a new formal theory of truth. The theory does not incorporate contradictions and is not substructural, but deviates from classical logic significantly, and endorses principles like 'No sentence is both true and false' and 'No sentence is neither true nor false'. The book starts with an introduction to the paradoxes, suitable for newcomers to the subject, before presenting its approach. Four versions of the theory are covered, extending the theory to a determinacy operator and to a full first-order language with quantifiers. Each includes all Tarskian biconditionals that can be formulated in its language. The author uses original methods to prove the consistency of each version and compares the theory to alternative non-classical theories, including Field's paracomplete approach, Ripley's nontransitive system and Zardini's contraction-free calculus.

A Comparison Process for Mouse Pairs
  • John R. Steel
  • Published online:
    10 November 2022
    Print publication:
    24 November 2022
  • This book proves some important new theorems in the theory of canonical inner models for large cardinal hypotheses, a topic of central importance in modern set theory. In particular, the author 'completes' the theory of Fine Structure and Iteration Trees (FSIT) by proving a comparison theorem for mouse pairs parallel to the FSIT comparison theorem for pure extender mice, and then using the underlying comparison process to develop a fine structure theory for strategy mice. Great effort has been taken to make the book accessible to non-experts so that it may also serve as an introduction to the higher reaches of inner model theory. It contains a good deal of background material, some of it unpublished folklore, and includes many references to the literature to guide further reading. An introductory essay serves to place the new results in their broader context. This is a landmark work in inner model theory that should be in every set theorist's library.

Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond
  • Volume 1, Ordered Graphs and Distanced Graphs
  • Gregory Cherlin
  • Published online:
    25 June 2022
    Print publication:
    07 July 2022
  • This is the first of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. In this volume, Cherlin develops a complete classification of homogeneous ordered graphs and provides a full proof. He then proposes a new family of metrically homogeneous graphs, a weakening of the usual homogeneity condition. A general classification conjecture is presented, together with general structure theory and applications to a general classification conjecture for such graphs. It also includes introductory chapters giving an overview of the results and methods of both volumes, and an appendix surveying recent developments in the area. An extensive accompanying bibliography of related literature, organized by topic, is available online.

Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond
  • Volume 2, 3-Multi-graphs and 2-Multi-tournaments
  • Gregory Cherlin
  • Published online:
    25 June 2022
    Print publication:
    07 July 2022
  • This is the second of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. This volume continues the analysis of the first volume to 3-multi-graphs and 3-multi-tournaments, expansions of graphs and tournaments by the addition of a further binary relation. The opening chapter provides an overview of the volume, outlining the relevant results and conjectures. The author applies and extends the results of Volume I to obtain a detailed catalogue of such structures and a second classification conjecture. The book ends with an appendix exploring recent advances and open problems in the theory of homogeneous structures and related subjects.

Complexity of Infinite-Domain Constraint Satisfaction
  • Manuel Bodirsky
  • Published online:
    28 May 2021
    Print publication:
    10 June 2021
  • Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.

Large Cardinals, Determinacy and Other Topics
  • The Cabal Seminar, Volume IV
  • Volume 4
  • Edited by Alexander S. Kechris, Benedikt Löwe, John R. Steel
  • Published online:
    27 October 2020
    Print publication:
    05 November 2020
  • The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Large Cardinals, Determinacy and Other Topics is the final volume in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. This final volume contains Parts VII and VIII of the series. Part VII focuses on 'Extensions of AD, models with choice', while Part VIII ('Other topics') collects material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of the book collection of every set theorist.

Algorithmic Randomness
  • Progress and Prospects
  • Edited by Johanna N. Y. Franklin, Christopher P. Porter
  • Published online:
    07 May 2020
    Print publication:
    07 May 2020
  • The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.

Abstract Recursion and Intrinsic Complexity
  • Yiannis N. Moschovakis
  • Published online:
    23 November 2018
    Print publication:
    06 December 2018
  • This book presents and applies a framework for studying the complexity of algorithms. It is aimed at logicians, computer scientists, mathematicians and philosophers interested in the theory of computation and its foundations, and it is written at a level suitable for non-specialists. Part I provides an accessible introduction to abstract recursion theory and its connection with computability and complexity. This part is suitable for use as a textbook for an advanced undergraduate or graduate course: all the necessary elementary facts from logic, recursion theory, arithmetic and algebra are included. Part II develops and applies an extension of the homomorphism method due jointly to the author and Lou van den Dries for deriving lower complexity bounds for problems in number theory and algebra which (provably or plausibly) restrict all elementary algorithms from specified primitives. The book includes over 250 problems, from simple checks of the reader's understanding, to current open problems.

Descriptive Complexity, Canonisation, and Definable Graph Structure Theory
  • Martin Grohe
  • Published online:
    30 August 2017
    Print publication:
    17 August 2017
  • Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.

Logic Colloquium 2000
  • Edited by René Cori, Alexander Razborov, Stevo Todorčević, Carol Wood
  • Published online:
    27 June 2017
    Print publication:
    02 March 2005
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the nineteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Paris, France in July 2000. This meeting marked the centennial anniversary of Hilbert's famous lecture and was held in the same hall at La Sorbonne where Hilbert presented his problems. Three long articles, based on tutorials given at the meeting, present accessible expositions of developing research in model theory, computability, and set theory. The eleven subsequent papers present work from the research frontier in all areas of mathematical logic.

Logic Colloquium '01
  • Edited by Matthias Baaz, Sy-David Friedman, Jan Krajíček
  • Published online:
    31 March 2017
    Print publication:
    02 March 2005
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twentieth publication in the Lecture Notes in Logic series, contains the proceedings of the 2001 European Summer Meeting of the Association for Symbolic Logic, held at the Vienna University of Technology. Two long articles present accessible expositions on resolution theorem proving and the determinacy of long games. The remaining articles cover separate research topics in many areas of mathematical logic, including applications in computer science, proof theory, set theory, model theory, computability theory, linguistics and aspects of philosophy. This collection will interest not only mathematical logicians but also philosophical logicians, historians of logic, computer scientists, formal linguists and mathematicians working in algebra, abstract analysis and topology.

Reflections on the Foundations of Mathematics
  • Essays in Honor of Solomon Feferman
  • Edited by Wilfried Sieg, Richard Sommer, Carolyn Talcott
  • Published online:
    31 March 2017
    Print publication:
    02 March 2002
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought.

Logic Colloquium '98
  • Edited by Samuel R. Buss, Petr Hájek, Pavel Pudlák
  • Published online:
    31 March 2017
    Print publication:
    02 March 2000
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the thirteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic held at the University of Economics in Prague, August 9–15, 1988. It includes surveys and research from preeminent logicians. The papers in this volume range over all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy. This book will be of interest to all students and researchers in mathematical logic.

Logic Colloquium '02
  • Edited by Zoé Chatzidakis, Peter Koepke, Wolfram Pohlers
  • Published online:
    31 March 2017
    Print publication:
    02 March 2006
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-seventh publication in the Lecture Notes in Logic series, contains the proceedings of two conferences: the European Summer Meeting of the Association for Symbolic Logic and the Colloquium Logicum, held in Münster, Germany in August, 2002. This compilation of articles from some of the world's preeminent logicians spans all areas of mathematical logic, including philosophical logic and computer science logic. It contains expanded versions of a number of invited plenary talks and tutorials that will be of interest to graduate students and researchers in the field of mathematical logic.

Reverse Mathematics 2001
  • Edited by Stephen G. Simpson
  • Published online:
    31 March 2017
    Print publication:
    02 March 2005
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Reverse mathematics is a program of research in the foundations of mathematics, motivated by two foundational questions: 'what are appropriate axioms for mathematics?' and 'what are the logical strengths of particular axioms and particular theorems?' This volume, the twenty-first publication in the Lecture Notes in Logic series, contains twenty-four original research papers from respected authors that present exciting new developments in reverse mathematics and subsystems of second order arithmetic since 1998.

Model Theory of Stochastic Processes
  • Sergio Fajardo, H. Jerome Keisler
  • Published online:
    30 March 2017
    Print publication:
    02 March 2002
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourteenth publication in the Lecture Notes in Logic series, Fajardo and Keisler present new research combining probability theory and mathematical logic. It is a general study of stochastic processes using ideas from model theory, a key central theme being the question, 'When are two stochastic processes alike?' The authors assume some background in nonstandard analysis, but prior knowledge of model theory and advanced logic is not necessary. This volume will appeal to mathematicians willing to explore new developments with an open mind.

Nonstandard Methods and Applications in Mathematics
  • Edited by Nigel J. Cutland, Mauro Di Nasso, David A. Ross
  • Published online:
    30 March 2017
    Print publication:
    02 March 2006
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fifth publication in the Lecture Notes in Logic series, grew from a conference on Nonstandard Methods and Applications in Mathematics held in Pisa, Italy from 12–16 June, 2002. It contains ten peer-reviewed papers that aim to provide something more timely than a textbook, but less ephemeral than a conventional proceedings. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. These articles consider the foundations of the subject, as well as its applications to pure and applied mathematics and mathematics education.

Logic in Tehran
  • Edited by Ali Enayat, Iraj Kalantari, Mojtaba Moniri
  • Published online:
    30 March 2017
    Print publication:
    02 March 2006
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-sixth publication in the Lecture Notes in Logic series, contains the proceedings of the 'Workshop and Conference on Logic, Algebra and Arithmetic' held at the Institute for Studies in Theoretical Physics and Mathematics (IPM) in Tehran, Iran in October, 2003. These papers are mostly revised and expanded versions of those that were originally presented at the meeting and address all areas of mathematical logic. The book also includes a short history of mathematical logic in Iran.

Logic Colloquium '99
  • Edited by Jan Van Eijck, Vincent Van Oostrom, Albert Visser
  • Published online:
    30 March 2017
    Print publication:
    02 March 2004
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the seventeenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Utrecht, The Netherlands in August, 1999. It includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in geometric model theory and the descriptive set theory of group actions. The other articles cover current research topics in all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy.

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