The Schröder-Bernstein property for $a$-saturated models
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- by John Goodrick and Michael C. Laskowski PDF
- Proc. Amer. Math. Soc. 142 (2014), 1013-1023 Request permission
Abstract:
A first-order theory $T$ has the Schröder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that $T$ has an expansion by constants with the SB property if and only if $T$ is superstable and non-multidimensional. We also prove that among superstable theories $T$, the class of $a$-saturated models of $T$ has the SB property if and only if $T$ has no nomadic types.References
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Additional Information
- John Goodrick
- Affiliation: Departamento de Matemáticas, Universidad de los Andes, Carrera 1 No. 18A-10, 111711 Bogotá, Colombia
- Email: jr.goodrick427@uniandes.edu.co
- Michael C. Laskowski
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- Email: mcl@math.umd.edu
- Received by editor(s): February 29, 2012
- Received by editor(s) in revised form: April 15, 2012
- Published electronically: December 10, 2013
- Additional Notes: The first author was partially supported by a grant from the Facultad de Ciencias, Universidad de los Andes, and by a travel grant from MSRI to attend the BIRS workshop on Neostability Theory (January 29–February 4, 2012).
The second author was partially supported by NSF grant DMS-0901336. - Communicated by: Julia Knight
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 1013-1023
- MSC (2010): Primary 03C45
- DOI: https://doi.org/10.1090/S0002-9939-2013-11844-7
- MathSciNet review: 3148535