Free Elementary Categories, Elementary Toposes (Oxford Logic Guides Book 21)
Description Elementary Categories, Elementary Toposes (Oxford Logic Guides Book 21)
The book covers elementary aspects of category theory and topos theory for graduate students in mathematics, computer science, and logic; it has few mathematical prerequisites, and uses categorical methods throughout, rather than beginning with set theoretical foundations. Working with key concepts such as Cartesian closedness, adjunctions, regular categories, and the internal logic of a topos, the book features full statements and elementary proofs for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Other chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis.
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Elementary Categories, Elementary Toposes (Oxford Logic ~ : Elementary Categories, Elementary Toposes (Oxford Logic Guides) (9780198514732): McLarty, Colin: Books
OXFORD LOGIC GUIDES - www.andrew.cmu.edu ~ OXFORD LOGIC GUIDES Available books in the series: 10. Michael Hallett: Cantorian set theory and limitation of size 17. Stewart Shapiro: Foundations without foundationalism 18. John P. Cleave: A study of logics 21. C. McLarty: Elementary categories, elementary toposes 22. R.M. Smullyan: Recursion theory for metamathematics 23.
Oxford Logic Guides - Oxford University Press ~ The Oxford Logic Guides is an outstanding series for logicians, mathematicians, computer scientists and philosophers which fosters in-depth knowledge and interdisciplinary studies alike. It includes texts and monographs providing material for the study of logic at an intermediate level along with authoritative reference works.
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Introduction to Logic and to the Methodology of the ~ Introduction to Logic and to the Methodology of the Deductive Sciences Alfred Tarski , Jan Tarski Classic undergraduate text sharpens students' grasp of the deductive method, including variables, sentential calculus, theory of identity, more.
Topos Theory (Dover Books on Mathematics): Johnstone, P.T ~ Barr and Wells TOPOSES, TRIPLES, AND THEORIES uses the most efficient tools to get at the central theorems. But no other book goes as concisely and comprehensively to all the aspects of toposes as this one. Category theory, algebra, logic, arithmetic, geometry, and cohomology all come in, in a well chosen perspective.
From (Paraconsistent) Topos Logic to Universal (Topos) Logic ~ In this chapter, I describe how complement toposes, with their paraconsistent internal logic, lead to a more abstract theory of topos logic. Béziau’s work in Universal Logic – including his ideas on logical structures, axiomatic emptiness and on logical many-valuedness – is central in this shift and therefore it is with great pleasure .
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Prática - USP ~ [2] F. Borceux , ``Handbook of Categorical Algebra 3: Categories of Sheaves'', Encyclopedia of Mathematics and its Apllications n.52, Cambridge University Press, 1994. [3] R.I. Goldblatt. ``Topoi: the categorical analysis of logic'', Studies in Logic and the Foundations of Math. Vol 98, North Holland, 1979.
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Set Theory - John L. Bell - Oxford University Press ~ This second edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century - the independence of the continuum hypothesis and the axiom of choice.
axiom - Wiktionary ~ (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved. 1748 January, R. M., “To the Gent. who Signs Verax, V[olume] 17 p[age] 573. In Answer to His Defence of Mr Lyttelton's Expression, that Matter is not Inherent in the Deity.”, in “Sylvanus .
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Elementary science textbooks : their contents, text ~ Elementary Science Textbooks 10 Considerateness Structure. Each category for assessing a text's considerateness came from the Anderson and Armbruster (1984) guidelines. In this stage of the analysis, we were actually searching for examples of "inconsiderate text," or more specifically, illogical structure.
The Evil Twin: The Basics of Complement-Toposes / SpringerLink ~ This paper is conceptually the first one of a tetralogy gathering up my logico-philosophical investigations on topos logic, deeply motivated by the philosophy behind Universal Logic: The other papers are [12, 15, 16], in that order.However, insofar as each paper is self-contained for it can be read independently, the reader might find several similarities between them in their introductions .
Logic in Elementary Mathematics (eBook) - Dover Books ~ This accessible, applications-related introductory treatment explores some of the structure of modern symbolic logic useful in the exposition of elementary mathematics. Topics include axiomatic structure and the relation of theory to interpretation. No prior training in logic is necessary, and numerous examples and exercises aid in the mastery of the language of logic. 1959 edition.
9780199237180: Category Theory (Oxford Logic Guides, 52 ~ Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied.
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