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Author:
Publisher: Academic Press
ISBN: 008087343X
Category : Mathematics
Languages : en
Pages : 237
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Book Description
Simplified Independence Proofs
Author:
Publisher: Academic Press
ISBN: 008087343X
Category : Mathematics
Languages : en
Pages : 237
Get Book Here
Book Description
Simplified Independence Proofs
Author: K. Kunen
Publisher: Elsevier
ISBN: 0080570585
Category : Mathematics
Languages : en
Pages : 330
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Book Description
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.
Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
ISBN:
Category : Copyright
Languages : en
Pages : 1938
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Book Description
Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3662223430
Category : Mathematics
Languages : en
Pages : 194
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Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author: John Lane Bell
Publisher: Clarendon Press
ISBN: 9780198532415
Category : Science
Languages : en
Pages : 165
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Book Description
Author: Jan Grabowski
Publisher: Springer
ISBN: 3540460632
Category : Computers
Languages : en
Pages : 277
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Book Description
This volume contains the proceedings of the First International Workshop on Algebraic and Logic Programming held in Gaussig (German Democratic Republic) from November 14 to 18, 1988. The workshop was devoted to Algebraic Programming, in the sense of programming by algebraic specifications and rewrite rule systems, and Logic Programming, in the sense of Horn clause specifications and resolution systems. This includes combined algebraic/logic programming systems, mutual relations and mutual implementation of programming paradigms, completeness and efficiency considerations in both fields, as well as related topics.
Author: Yu. I. Manin
Publisher: Springer Science & Business Media
ISBN: 1441906150
Category : Mathematics
Languages : en
Pages : 389
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Book Description
1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.
Author: H.W. Gottinger
Publisher: Springer Science & Business Media
ISBN: 9400998384
Category : Social Science
Languages : en
Pages : 340
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Book Description
Ethics, as one of the most respectable disciplines of philosophy, has undergone a drastic and revolutionary change in recent time. There are three main trends of this development. The first trend can be described as a tendency towards a rigorous formal and analytical language. This means simply that ethics has created beside its own formalized set theoretical language a variety of new formalized, logical and mathemati cal methods and concepts. Thus ethics has become a formalized meta or epidiscipline which is going to replace the traditional concepts, principles and ethical methods in the realm of social sciences. It is clear that a formalized form of ethics can be used more easily in social, economic and political theories if there are ethical conflicts to be solved. This first trend can be regarded as a conditio sine qua non for application in, and imposing ethical solutions on, social scientific theories. The second trend may be characterized as an association- or unification-tendency of a formalized and analytical ethics with decision theory. Decision theory as a new interdiscipline of social sciences is actually an assemblage of a variety of subtheories such as value-utility theory, game theory, collective decision theory, etc. Harsanyi has called this complex of subtheories a general theory of human behavior. Analytical or formal ethics is actually using this general theory of human behavior as a vehicle simply because this theory deals from the beginning with conflict solution, i. e.
Author: A.G. Kusraev
Publisher: Springer Science & Business Media
ISBN: 9401593493
Category : Mathematics
Languages : en
Pages : 456
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Book Description
The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants. Loosely speaking, the idea can be expressed as follows. If an operator (equation) under study is dominated by another operator (equation), called a dominant or majorant, then the properties of the latter have a substantial influence on the properties of the former . Thus, operators or equations that have "nice" dominants must possess "nice" properties. In other words, an operator with a somehow qualified dominant must be qualified itself. Mathematical tools, putting the idea of domination into a natural and complete form, were suggested by L. V. Kantorovich in 1935-36. He introduced the funda mental notion of a vector space normed by elements of a vector lattice and that of a linear operator between such spaces which is dominated by a positive linear or monotone sublinear operator. He also applied these notions to solving functional equations. In the succeedingyears many authors studied various particular cases of lattice normed spaces and different classes of dominated operators. However, research was performed within and in the spirit of the theory of vector and normed lattices. So, it is not an exaggeration to say that dominated operators, as independent objects of investigation, were beyond the reach of specialists for half a century. As a consequence, the most important structural properties and some interesting applications of dominated operators have become available since recently.
Author: Anne S. Troelstra
Publisher: Springer
ISBN: 3540378065
Category : Mathematics
Languages : en
Pages : 518
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Book Description
