substructure
Let Σ be a fixed signature, and 𝔄 and 𝔅 structures
for Σ. We say 𝔄 is a substructure of 𝔅, denoted 𝔄⊆𝔅, if for all x∈𝔄 we have x∈𝔅, and the inclusion map
i:𝔄→𝔅:x↦x is an embedding
.
When 𝔄 is a substructure of 𝔅, we also say that 𝔅 is an extension of 𝔄.
A submodel 𝔄 of a model 𝔅 of a (first-order) language ℒ if 𝔄 is a model of ℒ and 𝔄 is a substructure of 𝔅.
Title | substructure |
---|---|
Canonical name | Substructure |
Date of creation | 2013-03-22 13:50:32 |
Last modified on | 2013-03-22 13:50:32 |
Owner | almann (2526) |
Last modified by | almann (2526) |
Numerical id | 6 |
Author | almann (2526) |
Entry type | Definition |
Classification | msc 03C07 |
Synonym | submodel |
Related topic | StructuresAndSatisfaction |
Defines | extension |