Toposes and Local Set Theories: An Introduction | Dover Mathematics Books | Perfect for Advanced Math Studies & Research

$10.49

$13.99

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Toposes and Local Set Theories: An Introduction | Dover Mathematics Books | Perfect for Advanced Math Studies & Research

Toposes and Local Set Theories: An Introduction | Dover Mathematics Books | Perfect for Advanced Math Studies & Research

$10.49

$13.99

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Description

Topos theory has led to unexpected connections between classical and constructive mathematics. This text explores Lawvere and Tierney's concept of topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. A virtually self-contained introduction, this volume presents toposes as the models of theories — known as local set theories — formulated within a typed intuitionistic logic.The introductory chapter explores elements of category theory, including limits and colimits, functors, adjunctions, Cartesian closed categories, and Galois connections. Succeeding chapters examine the concept of topos, local set theories, fundamental properties of toposes, sheaves, locale-valued sets, and natural and real numbers in local set theories. An epilogue surveys the wider significance of topos theory, and the text concludes with helpful supplements, including an appendix, historical and bibliographical notes, references, and indexes.

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Reviews

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John L Bell is one of my favorite maths authors. He's also co-authored "Logical Options", another very good book about alternative logics.This book is what I've found to be the easiest route to understanding toposes and particularly how it relates to logic.The first chapter describes category theory but it's so dense that it's practically useless unless you already know category theory. I think a background in category theory is required to understand toposes. For this, I recommend:1. "Conceptual Mathematics" by Lawvere +2. "Basic Category Theory for Computer Scientists" by PierceOR a few other similar books such as Walters, or Barr & Wells.You also need some background in simple type theory, for which there are quite a few introductory books.There are a few other books about Topoi:1. Goldblatt claims to be introductory, but I actually find it VERY hard to follow.2. Bart Jacobs' "Categorical Logic and Type Theory" is actually easier than Goldblatt.3. This book is the best I found so far.I'm still reading the 3rd chapter. Will review more when I have time. Hope this helps!

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