On long increasing chains modulo flat ideals

TL;DR

This paper demonstrates the non-existence of certain long increasing sequences modulo flat ideals in the context of ordinal and set theory, specifically showing no omega_4-sequence exists in (omega_3)^{omega_3} modulo countable sets.

Contribution

It establishes new limitations on the length of increasing chains modulo flat ideals in a specific ordinal setting.

Findings

No omega_4-sequence exists in (omega_3)^{omega_3} modulo countable sets

Provides new insights into the structure of increasing chains modulo flat ideals

Advances understanding of ordinal sequences in set theory

Abstract

We prove that e.g. there is no omega_4-sequence in (omega_3)^{omega_3} increasing modulo the ideal of countable sets.