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

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Author: J. Friedman
Publisher:
ISBN:
Category : Electronic digital computers
Languages : en
Pages : 226

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Author: Kurt Gödel
Publisher:
ISBN:
Category :
Languages : en
Pages : 69

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Author: Danny A. J. Gómez Ramírez
Publisher: Springer Nature
ISBN: 3030502732
Category : Mathematics
Languages : en
Pages : 268

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Book Description
This volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called cognitive metamathematics, with the ultimate goal of achieving a global instance of concrete Artificial Mathematical Intelligence (AMI). In other words, AMI looks for the construction of an (ideal) global artificial agent being able to (co-)solve interactively formal problems with a conceptual mathematical description in a human-style way. It first gives formal guidelines from the philosophical, logical, meta-mathematical, cognitive, and computational points of view supporting the formal existence of such a global AMI framework, examining how much of current mathematics can be completely generated by an interactive computer program and how close we are to constructing a machine that would be able to simulate the way a modern working mathematician handles solvable mathematical conjectures from a conceptual point of view. The thesis that it is possible to meta-model the intellectual job of a working mathematician is heuristically supported by the computational theory of mind, which posits that the mind is in fact a computational system, and by the meta-fact that genuine mathematical proofs are, in principle, algorithmically verifiable, at least theoretically. The introduction to this volume provides then the grounding multifaceted principles of cognitive metamathematics, and, at the same time gives an overview of some of the most outstanding results in this direction, keeping in mind that the main focus is human-style proofs, and not simply formal verification. The first part of the book presents the new cognitive foundations of mathematics’ program dealing with the construction of formal refinements of seminal (meta-)mathematical notions and facts. The second develops positions and formalizations of a global taxonomy of classic and new cognitive abilities, and computational tools allowing for calculation of formal conceptual blends are described. In particular, a new cognitive characterization of the Church-Turing Thesis is presented. In the last part, classic and new results concerning the co-generation of a vast amount of old and new mathematical concepts and the key parts of several standard proofs in Hilbert-style deductive systems are shown as well, filling explicitly a well-known gap in the mechanization of mathematics concerning artificial conceptual generation.

Author: Nihon Sūgakkai
Publisher: MIT Press
ISBN: 9780262590204
Category : Mathematics
Languages : en
Pages : 1180

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Book Description
V.1. A.N. v.2. O.Z. Apendices and indexes.

Author: Kurt Gödel
Publisher:
ISBN: 0195039726
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 426

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Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 008095765X
Category : Computers
Languages : en
Pages : 341

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Sets, Models and Recursion Theory

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

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Book Description
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.