Classification Theory. Second Edition with a New Introduction PDF Download
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Author: Saharon Shelah
Publisher:
ISBN: 9781848904231
Category :
Languages : en
Pages : 0
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Book Description
This book is for readers who have learned about first order logic; Gödel's completeness theorem; the Löwenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones. The main test problem is the number of models of T of the infinite cardinal l as a function of l. This culminates in the so-called main gap theorem saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being stable or being super stable, where can we define dimension and weight, particularly for super stable theories.
Author: Saharon Shelah
Publisher:
ISBN: 9781848904231
Category :
Languages : en
Pages : 0
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Book Description
This book is for readers who have learned about first order logic; Gödel's completeness theorem; the Löwenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones. The main test problem is the number of models of T of the infinite cardinal l as a function of l. This culminates in the so-called main gap theorem saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being stable or being super stable, where can we define dimension and weight, particularly for super stable theories.
Author: S. Shelah
Publisher: Elsevier
ISBN: 008088024X
Category : Computers
Languages : en
Pages : 741
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Book Description
In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text. The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m
Author: K. Ueno
Publisher: Springer
ISBN: 3540374159
Category : Computers
Languages : en
Pages : 296
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Book Description
Author: Daniel N. Joudrey
Publisher: Bloomsbury Publishing USA
ISBN:
Category : Language Arts & Disciplines
Languages : en
Pages : 833
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Book Description
A new edition of this best-selling textbook reintroduces the topic of library cataloging from a fresh, modern perspective. Not many books merit an eleventh edition, but this popular text does. Newly updated, Introduction to Cataloging and Classification provides an introduction to descriptive cataloging based on contemporary standards, explaining the basic tenets to readers without previous experience, as well as to those who merely want a better understanding of the process as it exists today. The text opens with the foundations of cataloging, then moves to specific details and subject matter such as Functional Requirements for Bibliographic Records (FRBR), Functional Requirements for Authority Data (FRAD), the International Cataloging Principles (ICP), and RDA. Unlike other texts, the book doesn't presume a close familiarity with the MARC bibliographic or authorities formats; ALA's Anglo-American Cataloging Rules, 2nd Edition, revised (AACR2R); or the International Standard Bibliographic Description (ISBD). Subject access to library materials is covered in sufficient depth to make the reader comfortable with the principles and practices of subject cataloging and classification. In addition, the book introduces MARC, BIBFRAME, and other approaches used to communicate and display bibliographic data. Discussions of formatting, presentation, and administrative issues complete the book; questions useful for review and study appear at the end of each chapter.
Author: Saharon Shelah
Publisher:
ISBN: 9783662200940
Category :
Languages : en
Pages : 296
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Book Description
Author: William Charles Berwick Sayers
Publisher:
ISBN:
Category : Classification
Languages : en
Pages : 264
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Book Description
Author: Luciano da Fontoura Costa
Publisher:
ISBN: 9781351829526
Category : Electronic books
Languages : en
Pages : 662
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Book Description
Author: Luciano da Fontoura Costa
Publisher: CRC Press
ISBN: 9781420037555
Category : Computers
Languages : en
Pages : 688
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Book Description
Advances in shape analysis impact a wide range of disciplines, from mathematics and engineering to medicine, archeology, and art. Anyone just entering the field, however, may find the few existing books on shape analysis too specific or advanced, and for students interested in the specific problem of shape recognition and characterization, traditio
Author: Jonathan Kirby
Publisher: Cambridge University Press
ISBN: 1316732398
Category : Mathematics
Languages : en
Pages : 197
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Book Description
Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
Author: A.D. Gordon
Publisher: CRC Press
ISBN: 9781584888536
Category : Mathematics
Languages : en
Pages : 274
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Book Description
As the amount of information recorded and stored electronically grows ever larger, it becomes increasingly useful, if not essential, to develop better and more efficient ways to summarize and extract information from these large, multivariate data sets. The field of classification does just that-investigates sets of "objects" to see if they can be summarized into a small number of classes comprising similar objects. Researchers have made great strides in the field over the last twenty years, and classification is no longer perceived as being concerned solely with exploratory analyses. The second edition of Classification incorporates many of the new and powerful methodologies developed since its first edition. Like its predecessor, this edition describes both clustering and graphical methods of representing data, and offers advice on how to decide which methods of analysis best apply to a particular data set. It goes even further, however, by providing critical overviews of recent developments not widely known, including efficient clustering algorithms, cluster validation, consensus classifications, and the classification of symbolic data. The author has taken an approach accessible to researchers in the wide variety of disciplines that can benefit from classification analysis and methods. He illustrates the methodologies by applying them to data sets-smaller sets given in the text, larger ones available through a Web site. Large multivariate data sets can be difficult to comprehend-the sheer volume and complexity can prove overwhelming. Classification methods provide efficient, accurate ways to make them less unwieldy and extract more information. Classification, Second Edition offers the ideal vehicle for gaining the background and learning the methodologies-and begin putting these techniques to use.
