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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Schröder-Bernstein property for $ a$-saturated models


Authors: John Goodrick and Michael C. Laskowski
Journal: Proc. Amer. Math. Soc. 142 (2014), 1013-1023
MSC (2010): Primary 03C45
Published electronically: December 10, 2013
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11844-7
PII: S 0002-9939(2013)11844-7
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.