Effective prime uniqueness

Assuming the obvious definitions below, we show that a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to the theorem that there are two atomic decidable models which are n...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2017-12, Vol.145 (12), p.5363-5379
Main Authors: Peter Cholak, Charlie McCoy, C.S.C
Format: Article
Language:English
Subjects:
E. LOGIC AND FOUNDATIONS
Online Access:Get full text
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Summary:Assuming the obvious definitions below, we show that a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to the theorem that there are two atomic decidable models which are not computably isomorphic. We end with a section describing the implications of this result in reverse mathematics.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13675