Morley Rank Research Articles

Effective bounds on Morley rank

Effective bounds are obtained on the Morley rank of a 1-type, the Morley rank aT of a totally transcendental theory T, and the Blum density number dT of a quasi-totally transcendental theory T by means of type-omitting and absoluteness arguments over admissible sets. The above restrictions on T imply that aT and dr arc ordinals recursive in T. Every theory T is seen to have a universal domain hyperarithmetic in the hyperjump of T.