March 2011 Euler characteristics for strongly minimal groups and the eq-expansions of vector spaces
Vinicius Cifú Lopes
J. Symbolic Logic 76(1): 235-242 (March 2011). DOI: 10.2178/jsl/1294170998


We find the complete Euler characteristics for the categories of definable sets and functions in strongly minimal groups. Their images, which represent the Grothendieck semirings of those categories, are all isomorphic to the semiring of polynomials over the integers with nonnegative leading coefficient. As a consequence, injective definable endofunctions in those groups are surjective. For infinite vector spaces over arbitrary division rings, the same results hold, and more: We also establish the Fubini property for all Euler characteristics, and extend the complete one to the eq-expansion of those spaces while preserving the Fubini property but not completeness. Then, surjective interpretable endofunctions in those spaces are injective, and conversely. Our presentation is made in the general setting of multi-sorted structures.


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Vinicius Cifú Lopes. "Euler characteristics for strongly minimal groups and the eq-expansions of vector spaces." J. Symbolic Logic 76 (1) 235 - 242, March 2011.


Published: March 2011
First available in Project Euclid: 4 January 2011

zbMATH: 1220.03023
MathSciNet: MR2791346
Digital Object Identifier: 10.2178/jsl/1294170998

Rights: Copyright © 2011 Association for Symbolic Logic


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Vol.76 • No. 1 • March 2011
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