[PDF] First Order Categorical Logic eBook

Author : J. Lambek
Publisher : Cambridge University Press
Page : 308 pages
File Size : 14,52 MB
Release : 1988-03-25
Category : Mathematics
ISBN : 9780521356534

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Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

Author : B. Jacobs
Publisher : Gulf Professional Publishing
Page : 784 pages
File Size : 48,95 MB
Release : 2001-05-10
Category : Computers
ISBN : 9780444508539

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This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Author : Elaine M. Landry
Publisher : Oxford University Press
Page : 486 pages
File Size : 47,56 MB
Release : 2017
Category : Mathematics
ISBN : 019874899X

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This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.

Author : Boris Zilber
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 40,19 MB
Release :
Category : Mathematics
ISBN : 9780821897454

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The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.

Author : R. Goldblatt
Publisher : Elsevier
Page : 569 pages
File Size : 12,46 MB
Release : 2014-06-28
Category : Mathematics
ISBN : 148329921X

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The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.

Author : Tom Leinster
Publisher : Cambridge University Press
Page : 193 pages
File Size : 13,34 MB
Release : 2014-07-24
Category : Mathematics
ISBN : 1107044243

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A short introduction ideal for students learning category theory for the first time.

Author : Jonathan Kirby
Publisher : Cambridge University Press
Page : 197 pages
File Size : 47,82 MB
Release : 2019-04-18
Category : Mathematics
ISBN : 1316732398

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Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.