Remark 3.4 A Dedekind Finite Borel Set

TL;DR

This paper clarifies a correction to previous work by providing a proof that a certain remark about Dedekind finite Borel sets contradicts an earlier theorem, highlighting an inconsistency in the literature.

Contribution

It offers a proof of a remark by Karagila that corrects a contradiction in earlier published theorems about Dedekind finite Borel sets.

Findings

Proof of the remark confirming the contradiction

Clarification of the relationship between Dedekind finiteness and Borel sets

Correction of previous mathematical assertions

Abstract

Asaf Karagila pointed out that Remark 3.4 [1], directly contradicts Theorem 3.3 (c) [2] which was incorrectly stated. This note contains a proof of this remark. [1] Miller, Arnold W.; A Dedekind Finite Borel Set, Arch. Math. Logic 50 (2011), no. 1-2, 1--17. [2] Kanamori, A.; Pincus, D.; Does GCH imply AC locally?, Paul Erdos and his mathematics, II (Budapest, 1999), 413-426, Bolyai Soc. Math. Stud., 11, Janos Bolyai Math. Soc., Budapest, 2002.