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Department of Mathematics & Statistics













Model Theory Seminar | Carlos Cordoba (McMaster University)
	
 Nov 7, 2025 
 12:30PM to 1:30PM




































Date/Time

Date(s) - 07/11/2025
12:30 pm - 1:30 pm





Speaker: Carlos Cordoba


Location: Hamilton Hall, Room 410


Title: Classification of pseudofinite Abelian Groups and exact classes of finite abelian groups.


Abstract: In the context of Model theory, we say that a given structure is pseudofinite if it is elementary equivalent to an ultraproduct of finite structures. Colloquially this implies that the properties of the structure must be witnessed asymptotically by a family of finite structures. Previous work from  Eklof and Fischer (1972), and Basarab (1975), presented a characterization pseudofinite abelian groups from a model theoretic perspective, but no explicit construction of a pseudofinite group was presented nor a general form of such an abelian groups.




Using a characterization of the first order theory of abelian groups given by Szmielew’s theorem (1955) via Szmielew’s groups, which are direct sums of rather simple abelian groups, we worked towards an explicit classification of abelian groups by determining which Szmielew’s groups are pseudofinite.




During this seminar talk, I intend to present the work towards this explicit classification including closure results of pseudofinite abelian groups. Furthermore, I will mention ongoing work on Faux finite groups and asymptotic elementary classes.




This talk is based on joint work with Dr. Dario Garcia from Universidad de los Andes.