The problem of Horn and Tarski

TL;DR

This paper addresses a longstanding question in order theory by demonstrating that the concepts of -finite cc and -bounded cc orderings are not equivalent, providing a negative answer to Horn and Tarski's 1948 problem.

Contribution

The paper provides the first counterexample showing the non-equivalence of -finite cc and -bounded cc orderings.

Findings

-finite cc and -bounded cc are not equivalent

Counterexample disproves Horn and Tarski's conjecture

Clarifies the relationship between these order properties

Abstract

In 1948 A. Horn and A. Tarski asked whether the notions of a \sigma-finite cc and a \sigma-bounded cc ordering are equivalent. We give a negative answer to this question.