Fraisse classes of graded relational structures

TL;DR

This paper explores the extension of Fraisse theory to graded relational structures, establishing conditions for constructing graded Fraisse limits and examining examples like weighted graphs and fuzzy orders.

Contribution

It introduces a framework for Fraisse classes in graded structures and demonstrates how to build their limits, expanding classical model theory.

Findings

Established conditions for graded Fraisse limits

Constructed examples including weighted graphs and fuzzy orders

Extended classical Fraisse theory to graded structures

Abstract

We study classes of graded structures satisfying the properties of amalgamation, joint embedding and hereditariness. Given appropriate conditions, we can build a graded analogue of the Fraisse limit. Some examples such as the class of all finite weighted graphs or the class of all finite fuzzy orders (evaluated on a particular countable algebra) will be examined.