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Basic Set Theory
  • Language: en
  • Pages: 418

Basic Set Theory

Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.

Foundations of Set Theory
  • Language: en
  • Pages: 415

Foundations of Set Theory

  • Type: Book
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  • Published: 1973-12-01
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  • Publisher: Elsevier

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.

Foundations of Set Theory
  • Language: en
  • Pages: 404

Foundations of Set Theory

  • Type: Book
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  • Published: 1973
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  • Publisher: Unknown

None

A Hierarchy of Formulas in Set Theory
  • Language: en
  • Pages: 79

A Hierarchy of Formulas in Set Theory

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Basic Set Theory
  • Language: en
  • Pages: 391

Basic Set Theory

  • Type: Book
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  • Published: 1979
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  • Publisher: Springer

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Abstract Set Theory
  • Language: en
  • Pages: 298

Abstract Set Theory

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Understanding the Infinite
  • Language: en
  • Pages: 262

Understanding the Infinite

An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common se...

Memories of the American Mathematical Society
  • Language: en
  • Pages: 88

Memories of the American Mathematical Society

  • Type: Book
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  • Published: Unknown
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  • Publisher: Unknown

None

Stochastic Dominance
  • Language: en
  • Pages: 517

Stochastic Dominance

  • Type: Book
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  • Published: 2015-10-31
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  • Publisher: Springer

This fully updated third edition is devoted to the analysis of various Stochastic Dominance (SD) decision rules. It discusses the pros and cons of each of the alternate SD rules, the application of these rules to various research areas like statistics, agriculture, medicine, measuring income inequality and the poverty level in various countries, and of course, to investment decision-making under uncertainty. The book features changes and additions to the various chapters, and also includes two completely new chapters. One deals with asymptotic SD and the relation between FSD and the maximum geometric mean (MGM) rule (or the maximum growth portfolio). The other new chapter discusses bivariate...

The Higher Infinite
  • Language: en
  • Pages: 555

The Higher Infinite

Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.