Download or read book The Consistency of the Continuum Hypothesis written by Kurt Gödel and published by . This book was released on 1964 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Consistency of the Continuum Hypothesis written by Kurt Gödel and published by . This book was released on 1940 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Set Theory and the Continuum Hypothesis written by Paul J. Cohen and published by Courier Corporation. This book was released on 2008-12-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Download or read book Set Theory and the Continuum Problem written by Raymond M. Smullyan and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.

Download or read book Kurt G del Collected Works Volume III written by Kurt Gödel and published by Oxford University Press, USA. This book was released on 1986 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Anyone interested in the life and work of Kurt Gödel, or in the history of mathematical logic in this century, is indebted to all of the contributors to this volume for the care with which they have presented Gödel's work. They have succeeded in using their own expertise to elucidate both the nature and significance of what Gödel and, in turn, mathematical logic have accomplished." --Isis (on volume I). The third volume brings togetherGödels unpublished essays and lectures.

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Download or read book Consistency proof for the generalized continuum hypothesis written by Kurt Gödel and published by . This book was released on 1939 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bertrand Russell Memorial Volume written by George W Roberts and published by Routledge. This book was released on 2013-12-19 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Volume XXII of twenty-two in a collection on 20th Century Philosophy. Originally published in 1979, this volume attempts to assess some of the achievements of Bertrand Russell in philosophy, logic and mathematics, ethics and politics.

Download or read book Kurt G del written by William D. Brewer and published by Springer Nature. This book was released on 2022-09-08 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: During his lifetime, Kurt Gödel was not well known outside the professional world of mathematicians, philosophers and theoretical physicists. Early in his career, for his doctoral thesis and then for his Habilitation (Dr.Sci.), he wrote earthshaking articles on the completeness and provability of mathematical-logical systems, upsetting the hypotheses of the most famous mathematicians/philosophers of the time. He later delved into theoretical physics, finding a unique solution to Einstein’s equations for gravity, the ‘Gödel Universe’, and made contributions to philosophy, the guiding theme of his life. This book includes more details about the context of Gödel’s life than are found in earlier biographies, while avoiding an elaborate treatment of his mathematical/scientific/philosophical works, which have been described in great detail in other books. In this way, it makes him and his times more accessible to general readers, and will allow them to appreciate the lasting effects of Gödel’s contributions (the latter in a more up-to-date context than in previous biographies, many of which were written 15–25 years ago). His work spans or is relevant to a wide spectrum of intellectual endeavor, and this is emphasized in the book, with recent examples. This biography also examines possible sources of his unusual personality, which combined mathematical genius with an almost childlike naiveté concerning everyday life, and striking scientific innovations with timidity and hesitancy in practical matters. How he nevertheless had a long and successful career, inspiring many younger scholars along the way, with the help of his loyal wife Adele and some of his friends, is a fascinating story in human nature.

Download or read book On the Consistency of the Generalized Continuum Hypothesis written by Ladislav Rieger and published by . This book was released on 1963 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Formalism and Beyond written by Godehard Link and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-09 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.

Download or read book Finitely Supported Mathematics written by Andrei Alexandru and published by Springer. This book was released on 2016-08-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors present an alternative set theory dealing with a more relaxed notion of infiniteness, called finitely supported mathematics (FSM). It has strong connections to the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel (ZF) set theory with atoms and to the theory of (generalized) nominal sets. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures, where the set of atoms is infinite (not necessarily countable as for nominal sets). In FSM, 'sets' are replaced either by `invariant sets' (sets endowed with some group actions satisfying a finite support requirement) or by `finitely supported sets' (finitely supported elements in the powerset of an invariant set). It is a theory of `invariant algebraic structures' in which infinite algebraic structures are characterized by using their finite supports. After explaining the motivation for using invariant sets in the experimental sciences as well as the connections with the nominal approach, admissible sets and Gandy machines (Chapter 1), the authors present in Chapter 2 the basics of invariant sets and show that the principles of constructing FSM have historical roots both in the definition of Tarski `logical notions' and in the Erlangen Program of Klein for the classification of various geometries according to invariants under suitable groups of transformations. Furthermore, the consistency of various choice principles is analyzed in FSM. Chapter 3 examines whether it is possible to obtain valid results by replacing the notion of infinite sets with the notion of invariant sets in the classical ZF results. The authors present techniques for reformulating ZF properties of algebraic structures in FSM. In Chapter 4 they generalize FM set theory by providing a new set of axioms inspired by the theory of amorphous sets, and so defining the extended Fraenkel-Mostowski (EFM) set theory. In Chapter 5 they define FSM semantics for certain process calculi (e.g., fusion calculus), and emphasize the links to the nominal techniques used in computer science. They demonstrate a complete equivalence between the new FSM semantics (defined by using binding operators instead of side conditions for presenting the transition rules) and the known semantics of these process calculi. The book is useful for researchers and graduate students in computer science and mathematics, particularly those engaged with logic and set theory.

Download or read book Commutative Algebra Volume II written by Oscar Zariski and published by Courier Dover Publications. This book was released on 2019-11-13 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second text in this two-book series extends the classical material of Volume I, which focuses on field theory and the ideal theory of Noetherian rings and Dedekind domains. The connection of Volume II's material to algebraic geometry is stressed throughout the presentation, making this book a practical introduction to some basic concepts and the arithmetical foundations of algebraic geometry. The opening chapter deals with properties of places and is followed by a chapter that explores the classical properties of polynomial and power series rings and their applications to algebraic geometry. The final chapter examines the theory of local rings, which provides the algebraic basis for the local study of algebraic and analytical varieties. Several helpful Appendixes conclude the text.

Download or read book Scientific and Technical Books in Print written by and published by . This book was released on 1972 with total page 1630 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Download or read book Kurt G del Collected Works Volume V written by Kurt Gödel and published by . This book was released on 2013-10 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century. These collected works form the only comprehensive edition of Gödel's work available and are designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy.

Download or read book Philosophy of Mathematics in the Twentieth Century written by Charles Parsons and published by Harvard University Press. This book was released on 2014-03-17 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century. Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl’s idea of a “vicious circle” in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell’s mathematical logic—Gödel’s first mature philosophical statement and an avowal of his Platonistic view. Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine’s early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam’s views on existence and ontology, especially in relation to logic and mathematics. Wang’s contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait’s axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.