On terms describing omitting types 1 and 2 - an improved version

TL;DR

This paper investigates the conditions under which omitting types 1 and 2 can be characterized by systems of linear identities involving at most two ternary terms, identifying a promising candidate system but leaving its effectiveness unresolved.

Contribution

It analyzes all possible linear identity systems on two ternary terms and identifies a specific system that implies omitting types 1 and 2, highlighting a direction for future research.

Findings

Identified a system of linear identities that implies omitting types 1 and 2.

Analyzed all possible systems on two ternary terms for this property.

Left open whether the identified system fully characterizes omitting types 1 and 2.

Abstract

In this paper we examine the possibility of describing omitting types 1 and 2 by two at most ternary terms and any number of linear identities. All possible cases of systems of linear identities on two at most ternary terms are being analyzed, and it is shown that only a single one of these systems might describe omitting types 1 and 2. However, we do not resolve whether it actually describes omitting mentioned types, but only prove that it implies this property, so this question is left for further examination.