On reducts of Hrushovski's construction - the non-collapsed case

Assaf Hasson; Omer Mermelstein

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arXiv · 1305.2155

On reducts of Hrushovski's construction - the non-collapsed case

Assaf Hasson·Omer Mermelstein

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Abstract

We show that the rank {\omega} structure obtained by the non-collapsed version of Hrushovski's amalgamation construction has a proper reduct. We show that this reduct is the Fra\"iss\'e-Hrushovski limit of its own age with respect to a pre-dimension function generalising Hrushovski's pre-dimension function. It follows that this reduct has a unique regular type of rank {\omega}, and we prove that its geometry is isomorphic to the geometry of the generic type in the original structure. We ask whether our reduct is bi-interpretable with the original structure and whether it, too, has proper reducts with the same geometry.

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BibTeX RIS

Assaf Hasson, Omer Mermelstein. 2013-05-09. On reducts of Hrushovski's construction - the non-collapsed case. https://arxiv.org/abs/1305.2155

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