Recursive spectra of flat strongly minimal theories
Uri Andrews, Omer Mermelstein · Proceedings of the American Mathematical Society · 2021
We show that for a model complete strongly minimal theory whose pregeometry is flat, the recursive spectrum (SRM( T T )) is either of the form [ 0 , α ) [0,\alpha ) for α ∈ ω + 2 \alpha \in \omega +2 or [ 0 , n ] ∪ { ω } [0,n]\cup \left \{\omega \right \} for n ∈ ω n\in \omega , or { ω } \{\omega \} , or contained in { 0 , 1 , 2 } \left \{0,1,2\right \} . Combined with previous results, this leaves precisely 4 sets for which it is not yet determined whether each is the spectrum of a model complete strongly minimal theory with a flat pregeometry.