This page focuses on finitary first order model theory of infinite structures.
The relative emphasis placed on the class of models of a theory as opposed to the class of definable sets within a model fluctuated in the … See more

Definable sets
In model theory, definable sets are important objects of study. For instance, in See more

Realising and omitting types
Constructing models that realise certain types and do not realise others is an important task in model theory. Not realising a type is … See more

A key factor in the structure of the class of models of a first-order theory is its place in the stability hierarchy.
A complete theory T is called See more

First-order logic
A first-order formula is built out of atomic formulas such as $${\displaystyle R(f(x,y),z)}$$ or $${\displaystyle y=x+1}$$ by means of the Boolean connectives $${\displaystyle \neg ,\land ,\lor ,\rightarrow }$$ See more

Basic notions
For a sequence of elements $${\displaystyle a_{1},\dots ,a_{n}}$$ of a structure $${\displaystyle {\mathcal {M}}}$$ and a subset A of $${\displaystyle {\mathcal {M}}}$$, one can consider the set of all first-order … See more

A theory was originally called categorical if it determines a structure up to isomorphism. It turns out that this definition is not useful, due to … See more