Initial segments of the degrees of size א1

Uri Abraham; Richard A. Shore

doi:10.1007/BF02772668

Initial segments of the degrees of size א₁

Uri Abraham, Richard A. Shore

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We settle a series of questions first raised by Yates at the Jerusalem (1968) Colloquium on Mathematical Logic by characterizing the initial segments of the degrees of unsolvability of size א₁: Every upper semi-lattice of size א₁ with zero, in which every element has at most countably many predecessors, is isomorphic to an initial segment of the Turing degrees.

Original language	English
Pages (from-to)	1-51
Number of pages	51
Journal	Israel Journal of Mathematics
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/BF02772668
State	Published - 1 Feb 1986

ASJC Scopus subject areas

General Mathematics

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10.1007/BF02772668

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abstract = "We settle a series of questions first raised by Yates at the Jerusalem (1968) Colloquium on Mathematical Logic by characterizing the initial segments of the degrees of unsolvability of size א1: Every upper semi-lattice of size א1 with zero, in which every element has at most countably many predecessors, is isomorphic to an initial segment of the Turing degrees.",

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AB - We settle a series of questions first raised by Yates at the Jerusalem (1968) Colloquium on Mathematical Logic by characterizing the initial segments of the degrees of unsolvability of size א1: Every upper semi-lattice of size א1 with zero, in which every element has at most countably many predecessors, is isomorphic to an initial segment of the Turing degrees.

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Initial segments of the degrees of size א₁

Abstract

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