PlanetMath: substructure

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substructure

(Definition)

Let $\Sigma$ be a fixed signature, and $\mathfrak{A}$ and $\mathfrak{B}$ structures for $\Sigma$ . We say $\mathfrak{A}$ is a substructure of $\mathfrak{B}$ , denoted $\mathfrak{A}\subseteq \mathfrak{B}$ , if for all $x \in \mathfrak{A}$ we have $x \in \mathfrak{B}$ , and the inclusion map $i\colon \mathfrak{A}\to \mathfrak{B}: x \mapsto x$ is an embedding.

"substructure" is owned by almann.

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Other names:

submodel

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Cross-references: embedding, inclusion map, structures, signature, fixed
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This is version 1 of substructure, born on 2003-08-12.
Object id is 4579, canonical name is Substructure.
Accessed 2482 times total.

Classification:

AMS MSC:

03C07 (Mathematical logic and foundations :: Model theory :: Basic properties of first-order languages and structures)

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