On reducts of Hrushovski's construction - the non-collapsed case
Logic
2013-05-10 v1
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.
Keywords
Cite
@article{arxiv.1305.2155,
title = {On reducts of Hrushovski's construction - the non-collapsed case},
author = {Assaf Hasson and Omer Mermelstein},
journal= {arXiv preprint arXiv:1305.2155},
year = {2013}
}