Recursive spectra of strongly minimal theories satisfying the Zilber Trichotomy
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- by Uri Andrews and Alice Medvedev PDF
- Trans. Amer. Math. Soc. 366 (2014), 2393-2417 Request permission
Abstract:
We conjecture that for a strongly minimal theory $T$ in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum of $T$: all countable models of $T$ are recursively presentable; none of them are recursively presentable; or only the zero-dimensional model of $T$ is recursively presentable. We prove this conjecture for disintegrated (formerly, trivial) theories and for modular groups. The conjecture also holds via known results for fields. The conjecture remains open for finite covers of groups and fields.References
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Additional Information
- Uri Andrews
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- MR Author ID: 924690
- Alice Medvedev
- Affiliation: Department of Mathematics, The City College of New York, New York, New York 10031
- Received by editor(s): January 11, 2012
- Received by editor(s) in revised form: June 6, 2012
- Published electronically: January 28, 2014
- Additional Notes: The second author was partially supported by NSF FRG DMS-0854998 grant.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 2393-2417
- MSC (2010): Primary 03C57, 03C10
- DOI: https://doi.org/10.1090/S0002-9947-2014-05897-2
- MathSciNet review: 3165643