Search Results: classification-theory-for-abstract-elementary-classes-studies-in-logic-series

Classification Theory for Abstract Elementary Classes

Author: Saharon Shelah

Publisher: N.A

ISBN: 9781904987710

Category: Mathematics

Page: 813

View: 6618

An abstract elementary class is a class of structures of the same vocabulary (like a class of rings, or a class of fields), with a partial order that generalizes the relation "A is a substructure (or an elementary substructure) of B." The requirements are that the class is closed under isomorphism, and that isomorphic structures have isomorphic (generalized) substructures; we also require that our classes share some of the most basic properties of elementary classes, like closure under unions of increasing chains of substructures. We would like to classify this general family; in the sense of proving dichotomies: either we can understand the structure of all models in our class or there are many to some extent. More specifically we would like to generalize the theory about categoricity and superstability to this context.

Logic Without Borders

Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics

Author: Åsa Hirvonen,Juha Kontinen,Roman Kossak,Andrés Villaveces

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 1614519323

Category: Philosophy

Page: 438

View: 6526

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

A Course in Mathematical Logic for Mathematicians

Author: Yu. I. Manin

Publisher: Springer Science & Business Media

ISBN: 1441906150

Category: Mathematics

Page: 384

View: 9034

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

Classification Theory

Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic Held in Chicago, Dec. 15-19, 1985

Author: John T. Baldwin

Publisher: Springer

ISBN: 3540480498

Category: Mathematics

Page: 508

View: 6813

Dependence Logic

Theory and Applications

Author: Samson Abramsky,Juha Kontinen,Jouko Väänänen,Heribert Vollmer

Publisher: Birkhäuser

ISBN: 3319318039

Category: Mathematics

Page: 276

View: 7417

In this volume, different aspects of logics for dependence and independence are discussed, including both the logical and computational aspects of dependence logic, and also applications in a number of areas, such as statistics, social choice theory, databases, and computer security. The contributing authors represent leading experts in this relatively new field, each of whom was invited to write a chapter based on talks given at seminars held at the Schloss Dagstuhl Leibniz Center for Informatics in Wadern, Germany (in February 2013 and June 2015) and an Academy Colloquium at the Royal Netherlands Academy of Arts and Sciences (March 2014). Altogether, these chapters provide the most up-to-date look at this developing and highly interdisciplinary field and will be of interest to a broad group of logicians, mathematicians, statisticians, philosophers, and scientists. Topics covered include a comprehensive survey of many propositional, modal, and first-order variants of dependence logic; new results concerning expressive power of several variants of dependence logic with different sets of logical connectives and generalized dependence atoms; connections between inclusion logic and the least-fixed point logic; an overview of dependencies in databases by addressing the relationships between implication problems for fragments of statistical conditional independencies, embedded multivalued dependencies, and propositional logic; various Markovian models used to characterize dependencies and causality among variables in multivariate systems; applications of dependence logic in social choice theory; and an introduction to the theory of secret sharing, pointing out connections to dependence and independence logic.

Logic and Algebra

Author: Weimin Han

Publisher: American Mathematical Soc.

ISBN: 082182984X

Category: Mathematics

Page: 285

View: 7796

This volume outlines current developments in model theory and combinatorial set theory and presents state-of-the-art research. Well-known researchers report on their work in model theory and set theory with applications to algebra. The papers of J. Brendle and A. Blass present one of the most interesting areas of set theory. Brendle gives a very detailed and readable account of Shelah's solution for the long-standing problem of $\mathrm{Con}(\mathfrak{d}

The Many Sides of Logic

Author: Walter Carnielli,Marcelo E. Coniglio,Itala M. L. D'Ottaviano

Publisher: N.A

ISBN: N.A

Category: Computers

Page: 586

View: 5572

The Many Sides of Logic'' is a volume containing a selection of the papers delivered at three simultaneous events held between 11-17 May 2008 in Paraty, RJ, Brazil, continuing a tradition of three decades of Brazilian and Latin-American meetings and celebrating the 30th anniversary of an institution congenital with the mature interest for logic, epistemology and history of sciences in Brazil: CLE 30 - 30th Anniversary of the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (UNICAMP) XV EBL -15th Brazilian Logic Conference XIV SLALM - 14th Latin-American Symposium on Mathematical Logic Several renowned logicians, philosophers and mathematicians gathered in colonial Paraty, a historic village on the Brazilian coast founded in the 17th Century and surrounded by the luscious Atlantic rain forest to deliver lectures and talks celebrating the many sides of logic: the philosophical, the mathematical, the computational, the historical, and the multiple facets therein. The topics of the joint conferences, well represented here, included philosophical and mathematical Logic and applications with emphasis on model theory and proof theory, set theory, non-classical logics and applications, history and philosophy of logic, philosophy of the formal sciences and issues on the foundations of mathematics. The events have been preceded by a Logic School planned for students and young researchers held at the UNICAMP campus in Campinas, SP.

Mathematica Japonicae

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6356

The Bulletin of Symbolic Logic

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 1385

Resources in Education (RIE), 1990

Abstracts Index

Author: ABC-CLIO, LLC

Publisher: Greenwood

ISBN: 9780897746335

Category:

Page: N.A

View: 2090

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 9111

Research in Education

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Education

Page: N.A

View: 1995

Das Denken von Kindern

Author: Robert S. Siegler

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486806424

Category: Psychology

Page: 560

View: 318

Bis in die jüngste Vergangenheit blieb uns der Zugang zu vielen der interessanten Aspekte des Denkens von Kindern verwehrt. Philosophen haben sich Jahrhunderte lang darum gestritten, ob Säuglinge die Welt als "strahlendes und dröhnendes Durcheinander" sehen oder ganz ähnlich wie ältere Kinder und Erwachsene. Erst mit der Entwicklung aufschlußreicher experimenteller Methoden in den vergangenen Jahren wurde die Antwort deutlich. Sogar Neugeborene sehen bestimmte Aspekte der Welt recht klar und mit 6 Monaten ähnelt die Wahrnehmung von Säuglingen der von Erwachsenen. Dies und andere Erkenntnisse über das Denken von Kindern sind Gegenstand dieses Buches.

Wie kleine Kinder schlau werden

selbständiges Lernen im Alltag

Author: John Caldwell Holt

Publisher: N.A

ISBN: 9783407228550

Category:

Page: 232

View: 2078

Ausgehend von der Beobachtung des kindlichen Spielens erläutert der Autor, wie Kinder denken und lernen.

Library & Information Science Abstracts

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Information science

Page: N.A

View: 5751

Exceptional Child Education Abstracts

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Special education

Page: N.A

View: 5314

Dissertation Abstracts International

The humanities and social sciences

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Humanities

Page: N.A

View: 9018

Subject Guide to Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 4664

Cumulative Subject Index to Psychological Abstracts

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Psychological abstracts

Page: N.A

View: 2356

Dissertation Abstracts

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Dissertations, Academic

Page: N.A

View: 9867

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