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Poor triviality and the sameness of Grothendieck semirings


Author: Vinicius Cifú Lopes
Journal: Proc. Amer. Math. Soc. 140 (2012), 1445-1448
MSC (2010): Primary 03C07; Secondary 03C52
Published electronically: July 28, 2011
MathSciNet review: 2869129
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Abstract: We provide a characterization of the complete theories, all of whose models have the same Grothendieck semiring as those in which a certain weaker version of piecewise definable triviality holds. We also list some examples and properties of this poor triviality.


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Vinicius Cifú Lopes
Affiliation: Universidade Federal do ABC, Av. dos Estados, 5001, Santo André, SP 09210-971, Brazil
Email: vinicius@ufabc.edu.br, vinicius@alumni.illinois.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10977-8
Keywords: Definable triviality, Grothendieck semiring, Euler characteristic.
Received by editor(s): November 3, 2010
Received by editor(s) in revised form: December 27, 2010
Published electronically: July 28, 2011
Communicated by: Julia Knight
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.