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The least α for which E(α) is inadmissible

Part of: Computability and recursion theory

Published online by Cambridge University Press:  09 April 2009

M. R. R. Hoole
M. R. R. Hoole
Affiliation:
Department of Mathematics, University of Jaffna, Jaffna, Sri Lanka
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Abstract

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This paper attempts to classify the least ordinal α0 for which E(α0) (the E closure of α0 ∪ {α0}) is inadmissible. Among the result proved are (i)Lα0 = ZFC-; (ii)α0 is very large in comparison with the least ordinal satifying (i); (iii) (α0, α] marks precisely an ω-Gap, where α¯ = E(α0) ∩ ON; (iv) the Kr-sequence of α0 has length ω.

MSC classification

Secondary: 03D25: Recursively (computably) enumerable sets and degrees
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 2 , October 1986 , pp. 143 - 151
Copyright
Copyright © Australian Mathematical Society 1986

References

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