RECURSIVE SPECTRA OF FLAT STRONGLY MINIMAL THEORIES

Uri Andrews; Omer Mermelstein

doi:10.1090/proc/15613

RECURSIVE SPECTRA OF FLAT STRONGLY MINIMAL THEORIES

Uri Andrews, Omer Mermelstein

Research output: Contribution to journal › Article › peer-review

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, α) for α ∈ ω + 2 or [0, n] ∪ {ω} for n ∈ ω, or {ω}, 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.

Original language	English
Pages (from-to)	381-395
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	1
DOIs	https://doi.org/10.1090/proc/15613
State	Published - 1 Jan 2022
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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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, α) for α ∈ ω + 2 or [0, n] ∪ {ω} for n ∈ ω, or {ω}, 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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AB - 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, α) for α ∈ ω + 2 or [0, n] ∪ {ω} for n ∈ ω, or {ω}, 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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RECURSIVE SPECTRA OF FLAT STRONGLY MINIMAL THEORIES

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