On T-pseudofinite models of universal theories T
DOI:
https://doi.org/10.70474/fxyhwj58Keywords:
universal axiomatizable class of L-structures, theory of a class of L-structures, pseudofinite structure, T-pseudofinite structureAbstract
The concept of pseudofinite structures emerged in the 1960s as part of efforts to understand infinite structures that behave, in certain respects, like finite ones. A structure is pseudofinite if it satisfies every first-order sentence that holds in all finite structures of the same signature. This idea gained importance through works by Ax, who studied pseudofinite fields, and later by Hrushovski and others in the context of model-theoretic algebra. Pseudofiniteness has since played a key role in finite model theory and asymptotic classes. The article considers universal theories T, the number of isomorphism types of whose finite models is finite. It is proved that all cyclic submodels of a T-pseudofinite model of this theory are finite.
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