# Funcoid is a “Structure” in the Sense of Math Logic

A few seconds ago I realized that certain cases of pointfree funcoids can be described as a structure in the sense of mathematical logic, that is as a finite set of operations and relational symbols.

Precisely, if a pointfree funcoid is defined on a lattice (or semilattice) with a least element , then because a lattice (semilattice) is a relational structure defined by a set of propositional formula, then we have the following operations and relations:

- relation
- meet and join operations on our lattice
- the least element of the lattice (a constant symbol)

and identities:

- the standard identities of lattice considered as an algebraic structure (and also the obvious identities for the least element)

What are applications of the curious fact that every funcoid is a structure defined by propositional formulas? I don’t yet know.

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