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Author : M. Fitting
Publisher : Elsevier
Page : 328 pages
File Size : 45,6 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 9780080960319
Fundamentals of Generalized Recursion Theory
Author : Jens E. Fenstad
Publisher : Cambridge University Press
Page : 238 pages
File Size : 40,7 Mb
Release : 2017-03-02
Category : Mathematics
ISBN : 9781107168169
This volume presents a unified and coherent account of the many and various parts of general recursion theory.
Author : Jens Erik Fenstad,Peter G. Hinman
Publisher : Unknown
Page : 456 pages
File Size : 40,9 Mb
Release : 1972
Category : Recursive functions
ISBN : OCLC:465147662
Author : Jens Erik Fenstad
Publisher : Unknown
Page : 128 pages
File Size : 44,6 Mb
Release : 2016
Category : MATHEMATICS
ISBN : 1316754804
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the tenth publication in the Perspectives in Logic series, Jens E. Fenstad takes an axiomatic approach to present a unified and coherent account of the many and various parts of general recursion theory. The main core of the book gives an account of the general theory of computations. The author then moves on to show how computation theories connect with and unify other parts of general recursion theory. Some mathematical maturity is required of the reader, who is assumed to have some acquaintance with recursion theory. This book is ideal for a second course in the subject.
Author : René Cori,Alexander Razborov,Stevo Todorčević,Carol Wood
Publisher : Cambridge University Press
Page : 128 pages
File Size : 45,5 Mb
Release : 2017-03-30
Category : Mathematics
ISBN : 9781108756037
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the nineteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Paris, France in July 2000. This meeting marked the centennial anniversary of Hilbert's famous lecture and was held in the same hall at La Sorbonne where Hilbert presented his problems. Three long articles, based on tutorials given at the meeting, present accessible expositions of developing research in model theory, computability, and set theory. The eleven subsequent papers present work from the research frontier in all areas of mathematical logic.
Author : Giovanna Corsi,Maria Luisa Dalla Chiara,G. C. Ghirardi
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 46,6 Mb
Release : 1993
Category : Mathematics
ISBN : 0792317610
Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.
Author : G. Corsi,Maria Luisa Dalla Chiara,Giancarlo Ghirardi
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401124966
Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general `malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.
Author : Jens Erik Fenstad,R. O. Gandy,Gerald E. Sacks
Publisher : North-Holland
Page : 436 pages
File Size : 43,9 Mb
Release : 1978
Category : Electronic books
ISBN : UCAL:B4502354
Author : P. G. Hinman
Publisher : Springer
Page : 482 pages
File Size : 40,8 Mb
Release : 1978-05-01
Category : Mathematics
ISBN : 3540079041
At a recent meeting of logicians, one speaker complained - mainly, but perhaps not wholly, in jest - that logic is tightly controlled by a small group of people (the cabal) who exercise careful control over the release of new ideas to the general public (especially students) and indeed suppress some material com pletely. The situation is surely not so grim as this, but any potential reader of this book must have felt at some time that there is at least a minor conspiracy to keep new ideas inaccessible until the "insiders" have worked them over thoroughly. In particular he might well feel this way about the whole subject of Generalized Recursion Theory, which developed in the second half of the 1960s. The basic definitions and results on recursion involving functionals of higher type appeared in the monumental but extremely difficult paper Kleene [1959] and [1963]. Gandy [1967] gave another presentation ab initio, but the planned part II of this paper, as well as several other major advances in the subject, never appeared in print. For the theory of recursion on ordinals, the situation was even worse. Much of the basic material had appeared only in the abstracts Kripke [1964, 1964a], and although certain parts of the theory had been worked out in papers such as Kreisel-Sacks [1965] and Sacks [1967], there was no reasonably complete account of the basic facts of the subject in print.
Author : Elliot Mendelsohn
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461572886
This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.
Author : S. Abramsky,Dov M. Gabbay,T. S. E. Maibaum
Publisher : OUP Oxford
Page : 556 pages
File Size : 50,7 Mb
Release : 2001-01-25
Category : Computers
ISBN : 9780191546273
This handbook volume covers fundamental topics of semantics in logic and computation. The chapters (some monographic in length), were written following years of co-ordination and follow a thematic point of view. The volume brings the reader up to front line research, and is indispensable to any serious worker in the areas.
Author : Merlin Carl
Publisher : Walter de Gruyter GmbH & Co KG
Page : 343 pages
File Size : 53,5 Mb
Release : 2019-09-23
Category : Mathematics
ISBN : 9783110496154
Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.
Author : Solomon Feferman
Publisher : Oxford University Press, USA
Page : 353 pages
File Size : 49,7 Mb
Release : 1998
Category : Logic, Symbolic and mathematical
ISBN : 9780195080308
In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support. Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert, concentrating on three problems that have most to do with logic. Other chapters are devoted to the work and thought of Kurt Gödel, whose stunning results in the 1930s on the incompleteness of formal systems and the consistency of Cantors continuum hypothesis have been of utmost importance to all subsequent work in logic. Though Gödel has been identified as the leading defender of set-theoretical platonism, surprisingly even he at one point regarded it as unacceptable. In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no. This volume of important and influential work by one of the leading figures in logic and the foundations of mathematics is essential reading for anyone interested in these subjects.
Author : Joseph R. Shoenfield
Publisher : CRC Press
Page : 85 pages
File Size : 48,6 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9781351419413
This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.
Author : Chi Tat Chong,Liang Yu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 320 pages
File Size : 44,7 Mb
Release : 2015-08-17
Category : Mathematics
ISBN : 9783110275643
This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.