Definition:Subsignature

Definition

Let $\LL, \LL'$ be signatures for the language of predicate logic.

Then $\LL$ is said to be a subsignature of $\LL'$, denoted $\LL \subseteq \LL'$, if and only if, for each $n \in \N$:

$\map {\FF_n} \LL \subseteq \map {\FF_n} {\LL'}$

$\map {\PP_n} \LL \subseteq \map {\PP_n} {\LL'}$

where $\FF_n$ denotes the collection of $n$-ary function symbols, and $\PP_n$ denotes the collection of $n$-ary predicate symbols.

Supersignature

Let $\LL$ be a subsignature of $\LL'$.

Then $\LL'$ is said to be a supersignature of $\LL$, denoted:

$\LL' \supseteq \LL$

Also see

• Definition:Signature for Predicate Logic

• Definition:Expansion of Structure
• Definition:Reduct of Structure

Sources

• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\mathrm{II}.8$ Further Semantic Notions