Trivial Isomorphisms between Reduced Products

2023/07/13 by Ben de Bondt, De Bondt, Ben, Ilijas Farah +3 · 1 citation
Computer Science · Mathematics · #03E35 #03E50 #03E75 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2307.06731

openalex publication_date 2023/07/13 · openalex created_date 2023/07/15 · openalex updated_date 2026/07/28

Abstract

We introduce a general method for showing under weak forcing axioms that reduced products of countable models of a theory T have as few automorphisms as possible. We show that such forcing axioms imply that reduced products of countably infinite or finite fields, linear orders, trees, or random graphs have only trivial automorphisms. We also show that Todorčević's Open Colouring Axiom, OCA_T, implies that all automorphisms of P(ℕ)/Fin are trivial.

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• M ⁎ , N ⁎ , and H ⁎

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