Author: F.W. LawverePublisher: Springer
ISBN: 3540374957
Category : Mathematics
Languages : en
Pages : 352
Book Description
A Collection of Lectures by Variuos Authors
Model Theory and Topoi
Author: F.W. LawverePublisher: Springer
ISBN: 3540374957
Category : Mathematics
Languages : en
Pages : 352
Book Description
A Collection of Lectures by Variuos Authors
First Order Categorical Logic
Author: M. MakkaiPublisher: Springer
ISBN: 3540371001
Category : Mathematics
Languages : en
Pages : 317
Book Description
Topos Theory
Author: P.T. JohnstonePublisher: Courier Corporation
ISBN: 0486493369
Category : Mathematics
Languages : en
Pages : 401
Book Description
Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, and other subjects. 1977 edition.
Higher Topos Theory
Author: Jacob LuriePublisher: Princeton University Press
ISBN: 0691140480
Category : Mathematics
Languages : en
Pages : 944
Book Description
In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
Toposes and Local Set Theories
Author: John L. BellPublisher: Courier Corporation
ISBN: 0486462862
Category : Mathematics
Languages : en
Pages : 290
Book Description
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
A Functorial Model Theory
Author: Cyrus F. NouraniPublisher: CRC Press
ISBN: 1482231506
Category : Mathematics
Languages : en
Pages : 296
Book Description
This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Topoi
Author: R. GoldblattPublisher: Elsevier
ISBN: 148329921X
Category : Mathematics
Languages : en
Pages : 569
Book Description
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.
The Topos of Music
Author: Guerino MazzolaPublisher: Birkhäuser
ISBN: 303488141X
Category : Mathematics
Languages : en
Pages : 1310
Book Description
With contributions by numerous experts
Sketches of an Elephant: A Topos Theory Compendium
Author: P. T. JohnstonePublisher: Oxford University Press
ISBN: 9780198515982
Category : Computers
Languages : en
Pages : 836
Book Description
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.
Sheaves in Geometry and Logic
Author: Saunders Mac LanePublisher:
ISBN: 9783540977100
Category : Algebraische Geometrie - Garbentheorie
Languages : en
Pages : 627
Book Description
An introduction to the theory of toposes which begins with illustrative examples and goes on to explain the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.