Three Problems of "Distinction"

TL;DR

This paper formulates three key problems related to longest chains in an equivalence relation, highlighting their importance in estimating the size of quotient spaces, including reduced powers and ultrapowers.

Contribution

It introduces three novel problems concerning longest chains in equivalence relations and discusses their significance in the context of quotient space cardinality estimation.

Findings

Identification of three fundamental problems in equivalence relations.

Connection of these problems to estimating quotient space sizes.

Relevance to reduced powers and ultrapowers in set theory.

Abstract

Three problems related to the longest chains in an equivalence relation are formulated. Their relevance in estimating the cardinal of quotient spaces, and in particular, of reduced powers and ultrapowers, is indicated.