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Effective prime uniqueness


Authors: Peter Cholak and Charlie McCoy, C.S.C.
Journal: Proc. Amer. Math. Soc. 145 (2017), 5363-5379
MSC (2010): Primary 03D45; Secondary 03C57
DOI: https://doi.org/10.1090/proc/13675
Published electronically: June 16, 2017
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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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Additional Information

Peter Cholak
Affiliation: Department of Mathematics, University of Notre Dame
Email: cholak@nd.edu

Charlie McCoy, C.S.C.
Affiliation: Department of Mathematics, University of Portland
Email: mccoy@up.edu

DOI: https://doi.org/10.1090/proc/13675
Received by editor(s): July 20, 2015
Received by editor(s) in revised form: March 28, 2016, July 11, 2016, and January 3, 2017
Published electronically: June 16, 2017
Additional Notes: This work was partially supported by a grant from the Simons Foundation (#315283 to Peter Cholak).
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2017 American Mathematical Society