No minimal tall Borel ideal in the Kat\v{e}tov order

TL;DR

This paper proves that within the class of tall Borel ideals, there is no minimal element with respect to the Kat9tov order, resolving a previously open question.

Contribution

It establishes the non-existence of a minimal tall Borel ideal in the Kat9tov order, answering a specific open problem in the field.

Findings

No minimal tall Borel ideal exists in the Kat9tov order.

The result clarifies the structure of tall Borel ideals.

Answers an open question posed by the second author.

Abstract

Answering a question of the second listed author we show that there is no tall Borel ideal minimal among all tall Borel ideals in the Kat\v{e}tov order.