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Paul R. Halmos Naive Set Theory


Halmos begins, "Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer ... with the minimum of philosophical discourse and logical formalism". The mathematician, scientist, or engineer who needs to know the facts of set theory will find this crisp, clear, concise book, by a master expositor, ideal.

1327 RUR

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Paul R. Halmos Naive Set Theory


2011 Reprint of 1960 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Paul Richard Halmos (1916-2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor. "...He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." - "Philosophy and Phenomenological Research".

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Paul R. Halmos Lectures on Ergodic Theory


2013 Reprint of 1956 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. Paul Richard Halmos (1916 - 2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.

1009 RUR

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Paul R. Halmos Lectures on Boolean Algebras


2013 Reprint of 1963 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The theory of Boolean algebras is one of the most attractive parts of mathematics. On the one hand, Boolean algebras arise naturally in such diverse fields as logic, measure theory, topology, and ring theory, so that the study of these objects is motivated by important applications. At the same time, the theory which has been developed constitutes one of the most elegant parts of modern algebra. Finally, the subject still poses many challenging questions, some of which have considerable importance. A graduate student who wishes to study Boolean algebras will find several excellent books to smooth his way: for an introduction, the book by Halmos is probably the best of these monographs. It offers a quick route to the most attractive parts of the theory.

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Paul R. Halmos Algebraic Logic


2014 Reprint of 1962 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In "Algebraic Logic" Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra. This book addresses some of the problems of mathematical logic and the theory of polyadic Boolean algebras in particular. It is intended to be an efficient way of treating algebraic logic in a unified manner.

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Paul R. Halmos Introduction to Hilbert Space and the Theory of Spectral Multiplicity


2013 Reprint of 1951 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The subject matter of the book is funneled into three chapters: [1] The geometry of Hubert space; [2] the structure of self-adjoint and normal operators; [3] and multiplicity theory for a normal operator. For the last, an expert knowledge of measure theory is indispensable. Indeed, multiplicity theory is a magnificent measure-theoretic tour de force. The subject matter of the first two chapters might be said to constitute an introduction to Hilbert space, and for these, an a priori knowledge of classic measure theory is not essential. Paul Richard Halmos (1916-2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.

1055 RUR

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Paul R. Halmos Finite Dimensional Vector Spaces


2012 Reprint of 1942 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write "Finite Dimensional Vector Spaces." The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."

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Paul Ernst, R. F. Starzl Anthology of Sci-Fi V28, the Pulp Writers


The Anthology of Sci-Fi V28 is a collection of eight Sci-fi stories from two of the best writers of the past century. Included are: The Planet of Dread By R. F. Starzl, The World Behind the Moon By Paul Ernst, The Earthman's Burden By R. F. Starzl, If The Sun Died By R. F. Starzl, In the Orbit of Saturn By R. F. Starzl, The Planetoid of Peril By Paul Ernst, The Radiant Shell By Paul Ernst, Mask of Death By Paul Ernst.

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Judith Roitman Introduction to Modern Set Theory


Introduction to Modern Set Theory is designed for aone-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of illustrative examples both in the text and in the exercises, and the integration of consistency results and large cardinals into the text early on. This book is aimed at two audiences: studentswho are interested in studying set theory for its own sake, and studentsin other areas who may be curious about applications of set theory totheir field. In particular, great care is taken to develop the intuitions thatlie behind modern, as well as classical, set theory, and to connect settheory with the rest of mathematics.

952 RUR

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New Approaches to Classes and Concepts


Classifying objects --- thus collecting them into classes --- is anoperation both fundamental and common in everyday life as well as inscientific endeavours. Logic, philosophy, mathematics and computerscience analyse this activity by means of such notions as `class',`set', and `type'. Furthermore, according to the so-called ``logical(or naive) conception of classes", these notions are related to thenotion `concept' in that classes are considered `extensions' ofconcepts. This relationship, however, is a delicate one --- as wehave learned from the paradoxes of class theory. The contributions tothis volume shed new light both on concepts and classes and theirdelicate relationship. New and original approaches to these issues(e.g., map theory, epsilon-sets, intensional type theory, AFA settheory) are presented and discussed in the broader context of theirapplication to problems from informatics and linguistics. The focus ison such matters as unrestrictive comprehension, extensionality, therelationship between the notions of concept, class and extension, andon unfounded (circular and infinitely descending) patterns ofelementhood. These and related problems have always played a role inthe development of set theory and have always delivered motivation forthe development of unorthodox views and theories. This is alsodemonstrated in this volume by contributions dealing with the historyof Zermelo's axiomatization of set theory and Ackermann's class theory...

3489 RUR

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Paul Halmos Finite-Dimensional Vector Spaces


Master expositor Paul Halmos presents Linear Algebra in the pure axiomatic spirit. He writes "My purpose in this book is to treat linear transformations on finite dimensional vector spaces by the methods of more general theories. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications, and to do so in a language that gives away the trade secrets ...". This text is an ideal supplement to modern treatments of Linear Algebra. "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity....The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." --Zentralblatt für Mathematik.

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Kenneth Kunen The Foundations of Mathematics


Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general.This book is designed for students who plan to specialize in logic, as wellas for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginninggraduate-level course.There are three main chapters:Set Theory, Model Theory, and Recursion Theory.The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms.It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals.The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Löwenheim-Skolem Theorems,elementary submodels, model completeness, and applications to algebra.This chapter also continues the foundational issues begun in the set theory chapter.Mathematics can now be viewed as formal proofs from ZFC.Also, model theory leads to models of set theory.This includes a discussion of absoluteness, and an analysis of models such as H(κ) and R(γ).The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness...

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