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 ...
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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.
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Add this copy of Topoi: the Categorial Analysis of Logic to cart. $140.00, very good condition, Sold by Turn-The-Page Books rated 4.0 out of 5 stars, ships from Skyway, WA, UNITED STATES, published 1984 by Elsevier Science Ltd.
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Very Good. No Dust Jacket. Elsevier Science Ltd, 1984. Revised Edition. Tight and unmarked. Full black cloth binding. 551pp. Hardcover. Very Good/No Dust Jacket. 4to-over 9"-12" Tall.
Add this copy of Topoi: the Categorial Analysis of Logic (Volume 98) to cart. $198.00, fair condition, Sold by BooksRun rated 4.0 out of 5 stars, ships from Philadelphia, PA, UNITED STATES, published 1984 by North Holland.