Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Series
  3. Lecture Notes in Logic

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/.

  • Managing Editors: Paul Larson, Miami University
  • Editorial Boards: Zoe Chatzidakis, Ecole Normale Supérieure, Paris, Denis Hirschfeldt, University of Chicago, Leon Horsten, Universität Konstanz, Germany, Paulo Oliva, Queen Mary University of London, Martin Otto, Technische Universität, Darmstadt, Germany, Slawomir Solecki, Cornell University, New York

Refine search

Refine search

Content type:
Publication date:
Subject: Show more
Journals Show more
Publishers: Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

55 results in Lecture Notes in Logic

Page 2 of 3

Logic Colloquium '90
  • ASL Summer Meeting in Helsinki
  • Edited by Juha Oikkonen, Jouko Väänänen
  • Published online:
    24 March 2017
    Print publication:
    02 March 2017
  • 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 second publication in the Lecture Notes in Logic series, is the proceedings of the Association for Symbolic Logic meeting held in Helsinki, Finland, in July 1990. It contains eighteen papers by leading researchers, covering all fields of mathematical logic from the philosophy of mathematics, through model theory, proof theory, recursion theory, and set theory, to the connections of logic to computer science. The articles published here are still widely cited and continue to provide ideas for ongoing research projects.

Lectures on Infinitary Model Theory
  • David Marker
  • Published online:
    05 August 2016
    Print publication:
    27 October 2016
  • Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.

Logic and Algebraic Structures in Quantum Computing
  • Edited by Jennifer Chubb, Ali Eskandarian, Valentina Harizanov
  • Published online:
    05 June 2016
    Print publication:
    26 February 2016
  • Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.

Ordinal Definability and Recursion Theory
  • The Cabal Seminar, Volume III
  • Volume 3
  • Edited by Alexander S. Kechris, Benedikt Löwe, John R. Steel
  • Published online:
    05 December 2015
    Print publication:
    11 January 2016
  • The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third 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. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

A Guide to NIP Theories
  • Pierre Simon
  • Published online:
    05 July 2015
    Print publication:
    16 July 2015
  • The study of NIP theories has received much attention from model theorists in the last decade, fuelled by applications to o-minimal structures and valued fields. This book, the first to be written on NIP theories, is an introduction to the subject that will appeal to anyone interested in model theory: graduate students and researchers in the field, as well as those in nearby areas such as combinatorics and algebraic geometry. Without dwelling on any one particular topic, it covers all of the basic notions and gives the reader the tools needed to pursue research in this area. An effort has been made in each chapter to give a concise and elegant path to the main results and to stress the most useful ideas. Particular emphasis is put on honest definitions, handling of indiscernible sequences and measures. The relevant material from other fields of mathematics is made accessible to the logician.

Turing's Legacy
  • Developments from Turing's Ideas in Logic
  • Edited by Rod Downey
  • Published online:
    05 June 2014
    Print publication:
    01 May 2014
  • Alan Turing was an inspirational figure who is now recognised as a genius of modern mathematics. In addition to leading the Allied forces' code-breaking effort at Bletchley Park in World War II, he proposed the theoretical foundations of modern computing and anticipated developments in areas from information theory to computer chess. His ideas have been extraordinarily influential in modern mathematics and this book traces such developments by bringing together essays by leading experts in logic, artificial intelligence, computability theory and related areas. Together, they give insight into this fascinating man, the development of modern logic, and the history of ideas. The articles within cover a diverse selection of topics, such as the development of formal proof, differing views on the Church–Turing thesis, the development of combinatorial group theory, and Turing's work on randomness which foresaw the ideas of algorithmic randomness that would emerge many years later.

Effective Mathematics of the Uncountable
  • Edited by Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, Russell Miller
  • Published online:
    05 December 2013
    Print publication:
    31 October 2013
  • Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.

A Course in Model Theory
  • Katrin Tent, Martin Ziegler
  • Published online:
    05 June 2012
    Print publication:
    08 March 2012
  • This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.

Wadge Degrees and Projective Ordinals
  • The Cabal Seminar, Volume II
  • Edited by Alexander S. Kechris, Benedikt Löwe, John R. Steel
  • Published online:
    05 December 2011
    Print publication:
    01 December 2011
  • The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of 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. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

Set Theory, Arithmetic, and Foundations of Mathematics
  • Theorems, Philosophies
  • Edited by Juliette Kennedy, Roman Kossak
  • Published online:
    07 October 2011
    Print publication:
    01 September 2011
  • This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972–1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.

Quantifiers, Propositions and Identity
  • Admissible Semantics for Quantified Modal and Substructural Logics
  • Robert Goldblatt
  • Published online:
    07 September 2011
    Print publication:
    14 July 2011
  • Many systems of quantified modal logic cannot be characterised by Kripke's well-known possible worlds semantic analysis. This book shows how they can be characterised by a more general 'admissible semantics', using models in which there is a restriction on which sets of worlds count as propositions. This requires a new interpretation of quantifiers that takes into account the admissibility of propositions. The author sheds new light on the celebrated Barcan Formula, whose role becomes that of legitimising the Kripkean interpretation of quantification. The theory is worked out for systems with quantifiers ranging over actual objects, and over all possibilia, and for logics with existence and identity predicates and definite descriptions. The final chapter develops a new admissible 'cover semantics' for propositional and quantified relevant logic, adapting ideas from the Kripke–Joyal semantics for intuitionistic logic in topos theory. This book is for mathematical or philosophical logicians, computer scientists and linguists.

Simple Theories and Hyperimaginaries
  • Enrique Casanovas
  • Published online:
    05 March 2012
    Print publication:
    30 June 2011
  • This book is an up-to-date introduction to simple theories and hyperimaginaries, with special attention to Lascar strong types and elimination of hyperimaginary problems. Assuming only knowledge of general model theory, the foundations of forking, stability and simplicity are presented in full detail. The treatment of the topics is as general as possible, working with stable formulas and types and assuming stability or simplicity of the theory only when necessary. The author offers an introduction to independence relations as well as a full account of canonical bases of types in stable and simple theories. In the last chapters the notions of internality and analyzability are discussed and used to provide a self-contained proof of elimination of hyperimaginaries in supersimple theories.

Logic Colloquium 2007
  • Edited by Françoise Delon, Ulrich Kohlenbach, Penelope Maddy, Frank Stephan
  • Published online:
    01 March 2011
    Print publication:
    07 June 2010
  • 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.

A Framework for Priority Arguments
  • Manuel Lerman
  • Published online:
    04 August 2010
    Print publication:
    19 April 2010
  • This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs. The proposed framework presented isolates many of these unifying combinatorial principles and uses them to give shorter and easier-to-follow proofs of computability-theoretic theorems. Standard theorems of priority levels 1, 2, and 3 are chosen to demonstrate the framework's use, with all proofs following the same pattern. The last section features a new example requiring priority at all finite levels. The book will serve as a resource and reference for researchers in logic and computability, helping them to prove theorems in a shorter and more transparent manner.

Kurt Gödel
  • Essays for his Centennial
  • Edited by Solomon Feferman, Charles Parsons, Stephen G. Simpson
  • Published online:
    04 August 2010
    Print publication:
    19 April 2010
  • Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.

Logic Colloquium 2006
  • Edited by S. Barry Cooper, Herman Geuvers, Anand Pillay, Jouko Väänänen
  • Published online:
    28 January 2010
    Print publication:
    07 September 2009
  • 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, 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. The most topical areas of current research are covered: valued fields, Hrushovski constructions (from model theory), algorithmic randomness, relative computability (from computability theory), strong forcing axioms and cardinal arithmetic, large cardinals and determinacy (from set theory), as well as foundational topics such as algebraic set theory, reverse mathematics, and unprovability. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.

Games, Scales and Suslin Cardinals
  • The Cabal Seminar, Volume I
  • Edited by Alexander S. Kechris, Benedikt Löwe, John R. Steel
  • Published online:
    06 January 2010
    Print publication:
    15 September 2008
  • The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Games, Scales, and Suslin Cardinals is the first of 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. Focusing on the subjects of 'Games and Scales' (Part 1) and 'Suslin Cardinals, Partition Properties, and Homogeneity' (Part 2), each of the two sections is preceded by an introductory survey putting the papers into present context. This volume will be an invaluable reference for anyone interested in higher set theory.

Logic Colloquium 2004
  • Edited by Alessandro Andretta, Keith Kearnes, Domenico Zambella
  • Published online:
    05 July 2014
    Print publication:
    10 December 2007
  • The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of recent developments, and the rest of the papers are chosen to complement the invited talks. This volume includes surveys, tutorials, and selected research papers from the 2004 meeting. Highlights include a tutorial survey of the recent highpoints of universal algebra, written by a leading expert; explorations of foundational questions; and a quartet of model theory papers giving an excellent reflection of current work in model theory, from the most abstract aspect 'abstract elementary classes' to issues around p-adic integration.

Stable Domination and Independence in Algebraically Closed Valued Fields
  • Deirdre Haskell, Ehud Hrushovski, Dugald Macpherson
  • Published online:
    18 December 2009
    Print publication:
    10 December 2007
  • This book addresses a gap in the model-theoretic understanding of valued fields that had limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in many ways like the space of types in a stable theory. This part begins with an introduction to the key ideas of stability theory for stably dominated types. Part II continues with an outline of some classical results in the model theory of valued fields and explores the application of stable domination to algebraically closed valued fields. The research presented here is made accessible to the general model theorist by the inclusion of the introductory sections of each part.

Logic Colloquium 2005
  • Costas Dimitracopoulos, Ludomir Newelski, Dag Normann, John R. Steel
  • Published online:
    18 December 2009
    Print publication:
    03 December 2007
  • The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.

Page 2 of 3