# Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic

## TL;DR

This paper explores how classes of graded structures in mathematical fuzzy logic can be characterized syntactically, focusing on universal and existential sentences, and proves key amalgamation and preservation theorems.

## Contribution

It provides new syntactic characterizations of classes of structures in fuzzy logic and establishes foundational theorems like Los–Tarski and Chang–Los–Suszko in this context.

## Key findings

- Amalgamation results for structures valued on finite MTL-algebras
- Analogues of Los–Tarski preservation theorem
- Analogues of Chang–Los–Suszko preservation theorem

## Abstract

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Los--Tarski and the Chang--Los--Suszko preservation theorems follow.