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arXiv · 1805.03127

Higher amalgamation properties in stable theories

David M. Evans·Jonathan Kirby·Tim Zander
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Abstract

For a complete, stable theory $T$ we construct, in a reasonably canonical way, a related stable theory $T^*$ which has higher independent amalgamation properties over the algebraic closure of the empty-set. The theory $T^*$ is an algebraic cover of $T$ and we give an explicit description of the finite covers involved in the construction of $T^*$ from $T$. This follows an approach of E. Hrushovski. If $T$ is almost strongly minimal with a $0$-definable strongly minimal set, then we show that $T^*$ has higher amalgamation over any algebraically closed subset.

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BibTeXRIS

David M. Evans, Jonathan Kirby, Tim Zander. 2018-05-08. Higher amalgamation properties in stable theories. https://arxiv.org/abs/1805.03127

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