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arXiv · 2104.14550

Recursive spectra of flat strongly minimal theories

Uri Andrews·Omer Mermelstein
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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.

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Uri Andrews, Omer Mermelstein. 2021-04-29. Recursive spectra of flat strongly minimal theories. https://arxiv.org/abs/2104.14550

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