Quasifinite axiomatizability
Anand Pillay · 1996
Abstract We saw in Chapter 2 that totally categorical theories are not finitely axiomatizable. A slight extension of the proof yields non-finite axiomatizability of ω-categorical, ω-stable theories. At some point it was asked whether the only obstruction to the finite axiomatizability of, say, totally categorical theories was the non-finite expressibility of ‘there are infinitely many elements’, that is whether totally categorical theories could be finitely axiomatized modulo the ‘axiom of infinity’. In this chapter we see that this is true.