Non-Archimedean Analogue of Chase's Lemma

TL;DR

This paper develops a non-Archimedean version of Chase's lemma, extending previous work by removing cardinality restrictions and broadening the lemma's applicability in non-Archimedean frameworks.

Contribution

It formulates and verifies a non-Archimedean analogue of Chase's lemma, extending prior results to a more general non-Archimedean context.

Findings

Successfully formulated a non-Archimedean analogue of Chase's lemma.

Extended the lemma to non-Archimedean counterparts of existing extensions.

Removed restrictions of cardinality in the non-Archimedean setting.

Abstract

We formulate and verify a non-Archimedean analogue of Chase's lemma. Following the framework by K.\ Eda removing restriction of cardinality from analogy on direct product between countability and non-$\omega_1$-measurability, we extend the non-Archimedean analogue of Chase's lemma to a non-Archimedean counterpart of the extension by K.\ Eda of the extension by M.\ Dugas and B.\ Zimmermann-Huisgen of Chase's lemma.