Recursive spectra of flat strongly minimal theories

Andrews, Uri; Mermelstein, Omer

doi:10.1090/proc/15613

Recursive spectra of flat strongly minimal theories
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Proc. Amer. Math. Soc. 150 (2022), 381-395 Request permission

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 $[0,n]\cup \left \{\omega \right \}$ for $n\in \omega$, or $\{\omega \}$, or contained in $\left \{0,1,2\right \}$.

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.

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