Models and Games

Author: Jouko Väänänen

Publisher: Cambridge University Press

ISBN: 1139496336

Category: Mathematics

Page: N.A

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This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications.
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Algebraic Computability and Enumeration Models

Recursion Theory and Descriptive Complexity

Author: Cyrus F. Nourani

Publisher: CRC Press

ISBN: 1771882484

Category: Mathematics

Page: 310

View: 1561

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This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets. This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.
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An Invitation to Model Theory

Author: Jonathan Kirby

Publisher: Cambridge University Press

ISBN: 1107163889

Category: Mathematics

Page: 195

View: 9016

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An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.
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Generalized Descriptive Set Theory and Classification Theory

Author: Sy-David Friedman,Tapani Hyttinen, Vadim Kulikov

Publisher: American Mathematical Soc.

ISBN: 0821894757

Category: Mathematics

Page: 80

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Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.
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Probabilistic Theory of Mean Field Games with Applications I

Mean Field FBSDEs, Control, and Games

Author: René Carmona,François Delarue

Publisher: Springer

ISBN: 3319589202

Category: Mathematics

Page: 714

View: 3606

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This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
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Geometric Analysis

Author: Peter Li

Publisher: Cambridge University Press

ISBN: 1107020646

Category: Mathematics

Page: 406

View: 5947

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Basic techniques for researchers interested in the field of geometric analysis.
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Network Economics and the Allocation of Savings

A Model of Peering in the Voice-over-IP Telecommunications Market

Author: Philipp Servatius

Publisher: Springer Science & Business Media

ISBN: 9783642210969

Category: Business & Economics

Page: 297

View: 9281

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This book provides a game theoretic model of interaction among VoIP telecommunications providers regarding their willingness to enter peering agreements with one another. The author shows that the incentive to peer is generally based on savings from otherwise payable long distance fees. At the same time, termination fees can have a countering and dominant effect, resulting in an environment in which VoIP firms decide against peering. Various scenarios of peering and rules for allocation of the savings are considered. The first part covers the relevant aspects of game theory and network theory, trying to give an overview of the concepts required in the subsequent application. The second part of the book introduces first a model of how the savings from peering can be calculated and then turns to the actual formation of peering relationships between VoIP firms. The conditions under which firms are willing to peer are then described, considering the possible influence of a regulatory body.
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Conference Record of FPCA '95

SIGPLAN-SIGARCH-WG2.8 Conference on Functional Programming Languages and Computer Architecture : Papers Presented at the Conference, La Jolla, California, 25-28 June 1995

Author: N.A

Publisher: Assn for Computing Machinery

ISBN: N.A

Category: Computer architecture

Page: 333

View: 3740

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