The Consistency of the Axiom of Choice and of the Generalized Continuum-hypothesis with the Axioms of Set Theory PDF Download

Author: Kurt Gödel
Publisher: Princeton University Press
ISBN: 9780691079271
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 116

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Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 0486469212
Category : Mathematics
Languages : en
Pages : 196

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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.

Author: Yiannis N. Moschovakis
Publisher: American Mathematical Soc.
ISBN: 0821848135
Category : Mathematics
Languages : en
Pages : 521

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Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ``effective'' theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.

Author: Dana S. Scott
Publisher: American Mathematical Soc.
ISBN: 0821802453
Category : Mathematics
Languages : en
Pages : 482

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Author: J. N. Crossley
Publisher: Courier Corporation
ISBN: 0486151522
Category : Mathematics
Languages : en
Pages : 99

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A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.

Author: Elliott Mendelson
Publisher: CRC Press
ISBN: 1584888776
Category : Computers
Languages : en
Pages : 496

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Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Godel, Church

Author: Stephen Willard
Publisher: Courier Corporation
ISBN: 9780486434797
Category : Mathematics
Languages : en
Pages : 384

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Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

Author: James Whitehead
Publisher: Lulu.com
ISBN: 1326765868
Category : Religion
Languages : en
Pages : 120

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This book develops from Bad Music - The dogma of Modern Music/Art via Deleuze to Common music, Heidegger and the Ready at Hand and from this the idea of the unidentified individual, the Transcendent and The Divinity of Insatiable Desire.

Author: Kurt Gödel
Publisher: Princeton University Press
ISBN: 1400881633
Category : Mathematics
Languages : en
Pages : 69

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Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Göttingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond.

Author: Jon Barwise
Publisher: Cambridge University Press
ISBN: 1107168333
Category : Mathematics
Languages : en
Pages : 409

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This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.