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September 2007 Computable embeddings and strongly minimal theories
J. Chisholm, J. F. Knight, S Miller
J. Symbolic Logic 72(3): 1031-1040 (September 2007). DOI: 10.2178/jsl/1191333854

Abstract

Here we prove that if $T$ and $T'$ are strongly minimal theories, where $T'$ satisfies a certain property related to triviality and $T$ does not, and $T'$ is model complete, then there is no computable embedding of $Mod(T)$ into $Mod(T')$. Using this, we answer a question from [4], showing that there is no computable embedding of $VS$ into $ZS$, where $VS is the class of infinite vector spaces over $\mathbb{Q}$, and $ZS$ is the class of models of $Th(\mathbb{Z},S)$. Similarly, we show that there is no computable embedding of $ACF$ into $ZS$, where $ACF$ is the class of algebraically closed fields of characteristic 0.

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J. Chisholm. J. F. Knight. S Miller. "Computable embeddings and strongly minimal theories." J. Symbolic Logic 72 (3) 1031 - 1040, September 2007. https://doi.org/10.2178/jsl/1191333854

Information

Published: September 2007
First available in Project Euclid: 2 October 2007

zbMATH: 1127.03030
MathSciNet: MR2354913
Digital Object Identifier: 10.2178/jsl/1191333854

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 3 • September 2007
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