A generalization and a new proof of Plotkin's reduction theorem

TL;DR

This paper generalizes Plotkin's reduction theorem to broader categories with two special objects, simplifies its proof, and explores new applications in universal algebraic geometry.

Contribution

It introduces a generalized version of Plotkin's reduction theorem applicable to arbitrary categories with two special objects and provides a simpler proof along with new applications.

Findings

Generalization of Plotkin's reduction theorem to broader categories

Simplified proof of the generalized theorem

New applications in universal algebraic geometry

Abstract

It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories containing two special objects and in this case its proof becomes considerable more simple. This new proof and applications are the subject of the present paper.