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arXiv · 2307.06731

Trivial Isomorphisms between Reduced Products

Ben De Bondt·Ilijas Farah·Alessandro Vignati
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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 Todor\v{c}evi\'c's Open Colouring Axiom, $\mathsf{OCA}_{\mathrm{T}}$, implies that all automorphisms of $\mathcal{P}(\mathbb{N})/{\mathrm{Fin}}$ are trivial.

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Ben De Bondt, Ilijas Farah, Alessandro Vignati. 2023-07-13. Trivial Isomorphisms between Reduced Products. https://arxiv.org/abs/2307.06731

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