Finite axiomatizability and theories with trivial algebraic closure.
Dugald Macpherson · Notre Dame Journal of Formal Logic · 1991
It is shown that every quasi-finitely axiomatized complete theory with trivial algebraic closure has the strict order property or is the theory of an indiscernible set, and conjectured that every finitely axiomatized ω-categorical theory with infinite models has the strict order property.It is also shown that complete theories with trivial algebraic closure and (for example) no quantifier-free unstable formulas are rather limited.