J\'onsson posets

TL;DR

This paper investigates the structure of Jf3nsson posets, which are infinite ordered sets where every proper initial segment has smaller cardinality than the entire set, expanding understanding of their properties.

Contribution

It provides a detailed analysis of the structure of Jf3nsson posets, a class of infinite ordered sets with specific cardinality properties.

Findings

Characterization of Jf3nsson posets' structure

Conditions under which posets are Jf3nsson

Insights into the cardinality properties of initial segments

Abstract

According to Kearnes and Oman (2013), an ordered set $P$ is \emph{J\'onsson} if it is infinite and the cardinality of every proper initial segment of $P$ is strictly less than the cardinaliy of $P$. We examine the structure of J\'onsson posets.