What is an L-Structure? Now we double everything!

What are L-Structures

An L-structure M for some language L = {F0,...,Fn,P0,...,Pm,...,c1,...cq} is:

1. A set M called the domain or universe of M 

2. A function fM : Mnf → M for each f ∈ F 

3. A set RM ⊆ Mnr for each R ∈ P 

4. An element cM ∈ M for each c ∈ C

Where F , P, and C are subsets of L standing for function symbols, relation symbols, and constant symbols respectively. The cardinality of an L-structure M is the cardinality of its universe: |M|
It’s worth noting that Chang and Keisler refer to an L-structure M as a model for L, rather than an L-structure. However both Marker and Hodges call this an L-structure. (And, I believe, reserve the term “model” for L-structures that are models of some theory or set of sentences).

In other news: The formatting in this editor is a bit tricky… I’ve been writing these in Google docs and pasting them in here so I have a copy, but it looks like I may have to go the other way around. Darn :/