Recursive spectra of flat strongly minimal theories

Abstract

We show that for a model complete strongly minimal theory whose pregeometry is flat, the recursive spectrum (SRM($T$)) is either of the form $[0,\alpha )$ for $\alpha \in \omega +2$ or $[0,n]\cup \{\omega \}$ for $n\in \omega$, or $\{\omega \}$, or contained in $\{0,1,2\}$. 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.