Abstract:
Effective model theory is an area of logic that analyzes the effective content of the typical notions and
results of model theory and universal algebra. Typical notions in model theory and universal algebra
are languages and structures, theories and models, models and their submodels, automorphisms and
isomorphisms, embeddings and elementary embeddings. In this paper languages, structures, and models
are assumed to be countable.
There are many ways to introduce considerations of effectiveness into the area of model theory or
universal algebra. Here we will briefly explain considerations of effectiveness for theories and their models
on the one hand, and for just structures on the other hand.