Indifference to symmetry in Hrushovski's ab initio construction

DOI10.1016/J.APAL.2021.103040arXiv1603.05170MaRDI QIDQ6271553

Omer Mermelstein

Publication date: 16 March 2016

Abstract: Denote Hrushovski's non-collapsed ab initio construction for an $n$-ary relation by $mathcal{M}_{otsim}$ and the analogous construction for a symmetric $n$-ary relation by $mathcal{M}_{sim}$. We show that $mathcal{M}_{otsim}$ is isomorphic to a proper reduct of $mathcal{M}_{sim}$ and vice versa, and that the combinatorial pregeometries associated with both structures are isomorphic.

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Models with special properties (saturated, rigid, etc.) (03C50) Subgroups of symmetric groups (20B35) Other model constructions (03C30)

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