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Banach–Mazur games, comeager sets and degrees of unsolvability

Published online by Cambridge University Press:  24 October 2008

C. E. M. Yates
C. E. M. Yates
Affiliation:
University of Manchester
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Extract

This paper provides a framework for studying the general theory of the upper semi-lattice of degrees of unsolvability. A less obvious and more complicated extension of this framework has been initiated in our papers (17) and (18); these are concerned not with the general theory but with the Priority Method, for which a useful formal framework has long been sought. Our purpose here is partly to provide some background for these other papers, which should help explicate their less obvious aspects; but mainly we wish to illustrate the advantages of this framework from a purely expository point of view. There is an additional advantage in that a formal framework makes it possible to pose certain precise questions which were vague before, and even on occasion to answer them.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 2 , March 1976 , pp. 195 - 220
Copyright
Copyright © Cambridge Philosophical Society 1976

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