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arXiv · 1603.05170

Indifference to symmetry in Hrushovski's ab initio construction

Omer Mermelstein
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Abstract

Denote Hrushovski's non-collapsed ab initio construction for an $n$-ary relation by $\mathcal{M}_{\not\sim}$ and the analogous construction for a symmetric $n$-ary relation by $\mathcal{M}_{\sim}$. We show that $\mathcal{M}_{\not\sim}$ is isomorphic to a proper reduct of $\mathcal{M}_{\sim}$ and vice versa, and that the combinatorial pregeometries associated with both structures are isomorphic.

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Omer Mermelstein. 2016-03-16. Indifference to symmetry in Hrushovski's ab initio construction. https://arxiv.org/abs/1603.05170

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