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Infinite time Turing machines

Published online by Cambridge University Press:  12 March 2014

Joel David Hamkins  and
Andy Lewis
Joel David Hamkins
Affiliation:
Department of Mathematics, City University of New York, College of Staten Island, Staten Island, NY 10314., USA, E-mail: hamkins@postbox.csi.cuny.edu
Andy Lewis
Affiliation:
Department of Mathematics, Virginia Commonwealth University, Box #842014, Richmond, VA. 23284-2019, E-mail: amlewis@saturn.vcu.edu
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Abstract

We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. Every set. for example, is decidable by such machines, and the semi-decidable sets form a portion of the sets. Our oracle concept leads to a notion of relative computability for sets of reals and a rich degree structure, stratified by two natural jump operators.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 567 - 604
Copyright
Copyright © Association for Symbolic Logic 2000

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