Introduction to Axiomatic Set Theory, G. Takeuti; W.M. Zaring

Автор: Awodey, Steve
Название: Introduction to Category Theory (Paperback)
ISBN: 0199237182 ISBN-13(EAN): 9780199237180
Издательство: Oxford Academ
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Описание: A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.

Автор: Xiaodong Liu; Witold Pedrycz
Название: Axiomatic Fuzzy Set Theory and Its Applications
ISBN: 3642101461 ISBN-13(EAN): 9783642101465
Издательство: Springer
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Описание: This volume examines Axiomatic Fuzzy Sets (AFS), in which fuzzy sets and probability are treated in a unified and coherent fashion. It presents AFS as a rigorous mathematical theory as well as a flexible methodology for the development of intelligent systems.

Автор: Emily Carson; Renate Huber
Название: Intuition and the Axiomatic Method
ISBN: 9048170192 ISBN-13(EAN): 9789048170197
Издательство: Springer
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Описание: Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant`s theory of intuition to be obsolete.

Автор: David Marker
Название: Model Theory : An Introduction
ISBN: 1441931570 ISBN-13(EAN): 9781441931573
Издательство: Springer
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Автор: Yu. I. Manin; Alexei A. Panchishkin
Название: Introduction to Modern Number Theory
ISBN: 3642057977 ISBN-13(EAN): 9783642057977
Издательство: Springer
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Описание: It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. This substantially revised and expanded new edition contains several new sections, such as Wiles` proof of Fermat`s Last Theorem, and relevant techniques coming from a synthesis of various theories.

Автор: Barot Michael
Название: Introduction to the Representation Theory of Algebras
ISBN: 3319114743 ISBN-13(EAN): 9783319114743
Издательство: Springer
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Описание: and (iii) deeper theorems such as Gabriel`s Theorem, the trichotomy and the Theorem of Kac - all accompanied by further examples.Each section includes exercises to facilitate understanding.

Автор: Vladimir Kanovei; Michael Reeken
Название: Nonstandard Analysis, Axiomatically
ISBN: 3642060773 ISBN-13(EAN): 9783642060779
Издательство: Springer
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Описание: In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan- dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat- ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.

Автор: John Greenlees
Название: Axiomatic, Enriched and Motivic Homotopy Theory
ISBN: 1402018339 ISBN-13(EAN): 9781402018336
Издательство: Springer
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Описание: Consists of a series of expository articles on axiomatic, enriched and motivic homotopy theory arising out of a NATO Advanced Study Institute at the Isaac Newton Institute for the Mathematical Sciences in Cambridge, UK in September 2002.

Автор: Steven Roman
Название: An Introduction to the Language of Category Theory
ISBN: 3319419161 ISBN-13(EAN): 9783319419169
Издательство: Springer
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Описание: The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories.

Автор: K. Kunen
Название: Set Theory An Introduction To Independence Proofs,
ISBN: 0444868399 ISBN-13(EAN): 9780444868398
Издательство: Elsevier Science
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Описание: Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.