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The Categorial Analysis of Logic

Author: R. Goldblatt

Publisher: Elsevier


Category: Mathematics

Page: 565

View: 276

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.

Lecture Notes on Topoi and Quasitopoi

Author: Oswald Wyler

Publisher: World Scientific


Category: Mathematics

Page: 290

View: 938

Quasitopoi generalize topoi, a concept of major importance in the theory of Categoreis, and its applications to Logic and Computer Science. In recent years, quasitopoi have become increasingly important in the diverse areas of Mathematics such as General Topology and Fuzzy Set Theory. These Lecture Notes are the first comprehensive introduction to quasitopoi, and they can serve as a first introduction to topoi as well.

Classifying Spaces and Classifying Topoi

Author: Izak Moerdijk

Publisher: Springer


Category: Mathematics

Page: 98

View: 503

This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival- ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by "classifying" spaces. The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory.

Forcing and Classifying Topoi

Author: Andrej Ščedrov

Publisher: American Mathematical Soc.


Category: Mathematics

Page: 93

View: 511

Variable sets etendu and variable structure in topoi

Author: F. W. Lawvere



Category: Set theory

Page: 47

View: 818

Aristotele's Topics

Author: Paul Slomkowski

Publisher: BRILL


Category: Philosophy

Page: 218

View: 457

This work provides some interesting new results on the notion of the topos and the theory of hypothetical syllogisms in Aristotle based on an incisive interpretation of Aristotle's "Topics" and certain passages of the "Analytics."

Lattice theoretic and logical aspects of elementary topoi

Author: Christian Juul Mikkelsen



Category: Lattice theory

Page: 122

View: 998

A Place to Stand

Politics and Persuasion in a Working-Class Bar

Author: Julie Lindquist

Publisher: Oxford University Press


Category: Language Arts & Disciplines

Page: 216

View: 492

Linguists have become increasingly interested in examining how class culture is socially constructed and maintained through spoken language. Julie Lindquist's examination of the linguistic ethnography of a working-class bar in Chicago is an important and original contribution to the field. She examines how regular patrons argue about political issues in order to create a group identity centered around political ideology. She also shows how their political arguments are actually a rhetorical genre, one which creates a delicate balance between group solidarity and individual identity, as well as a tenuous and ambivalent sense of class identity.


Mapping the Middle in Spatial Thought

Author: Christian Abrahamsson

Publisher: U of Nebraska Press


Category: Philosophy

Page: 198

View: 624

"In Topoi/Graphein Christian Abrahamsson maps the paradoxical limit of the in-between to revealthat to be human is to know how tolive with the difference between the known and the unknown. Using filmic case studies, including CodeInconnu, Lord of the Flies, and Apocalypse Now,and focusing on key concerns developed in the works of the philosophers Deleuze, Olsson, and Wittgenstein, Abrahamsson starts within the notion of fixed spatiality, in whichhuman thought and action are anchored in the given of identity. He then movesthrough a social world in which spatiotemporal transformations are neitherfixed nor taken for granted. Finally he edges into the pure temporality that liesbeyond the maps of fixed points and social relations. Each chapter is organized into two subjects: topoi, orexcerpts from the films, and graphein, the author's interpretation ofpresented theoriesto mirror the displacements,transpositions, juxtapositions, fluctuations, and transformations between delimited categories. A landmark work in the study of human geography, Abrahamsson's book proposes that academic and intellectual attention should focus on the spatialization between meaning and its materialization in everyday life."

Model Theory and Topoi

Author: F.W. Lawvere

Publisher: Springer


Category: Mathematics

Page: 358

View: 285

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