Effective prime uniqueness

Cholak, Peter; Charlie McCoy, C.S.C.

doi:10.1090/proc/13675

Effective prime uniqueness
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by Peter Cholak and C.S.C. Charlie McCoy PDF

Proc. Amer. Math. Soc. 145 (2017), 5363-5379 Request permission

Abstract:

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.

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