In the context of mathematical logic, the term "model" was first applied in 1940 by the philosopher Willard Van Orman Quine, in a reference to mathematician Richard Dedekind (1831 … 展开

$${\displaystyle {\mathcal {A}}}$$ is called an (induced) substructure of $${\displaystyle {\mathcal {B}}}$$ if
• $${\displaystyle {\mathcal {A}}}$$ and
• the domain of 展开

Structures are sometimes referred to as "first-order structures". This is misleading, as nothing in their definition ties them to any specific logic, and in fact they are suitable as semantic objects both for very restricted fragments of first-order logic such as that used in … 展开

Formally, a structure can be defined as a triple $${\displaystyle {\mathcal {A}}=(A,\sigma ,I)}$$ consisting of a domain $${\displaystyle A,}$$ a signature $${\displaystyle \sigma ,}$$ and … 展开

Homomorphisms
Given two structures $${\displaystyle {\mathcal {A}}}$$ and $${\displaystyle {\mathcal {B}}}$$ of the same signature σ, a (σ-)homomorphism from 展开

Structures as defined above are sometimes called one-sorted structures to distinguish them from the more general many-sorted structures. A many-sorted structure can have an … 展开

Partial algebras
Both universal algebra and model theory study classes of (structures or) algebras that are defined by a … 展开