Products of pseudofinite structures
Paola D'Aquino, Angus Macintyre
TL;DR
This paper proves that the product of any family of pseudofinite structures remains pseudofinite, utilizing foundational results on products of first-order structures.
Contribution
It establishes that pseudofiniteness is preserved under arbitrary products of structures, extending previous understanding in model theory.
Findings
Products of pseudofinite structures are pseudofinite.
Utilizes Feferman-Vaught results on structure products.
Extends pseudofiniteness properties in model theory.
Abstract
We prove that any product of a family of pseudofinite structures is pseudofinite. The main tools are the fundamental results on products of first order structures due to Feferman and Vaught.
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Taxonomy
TopicsAdvanced Algebra and Logic