A Tame Generic Structure with Non-Algebraic Geometric Closure
Logic
2025-10-16 v3
Abstract
By providing a procedure to apply Hrushovski's amalgamation method to the setting of classes of infinite structures, we introduce the notion of \textit{paracollapsed} structures. We show that this approach provides existentially closed generic structures in which the geometric closure is not included in the algebraic closure while the resulting theory is decidable. We show that paracollapsed structures have the strict order property and .
Cite
@article{arxiv.2011.04034,
title = {A Tame Generic Structure with Non-Algebraic Geometric Closure},
author = {Somaye Jalili and Massoud Pourmahdian and Ali N. Valizadeh},
journal= {arXiv preprint arXiv:2011.04034},
year = {2025}
}
Comments
In this version we prove that the decidable theory of paracollapsed structures has SOP and TP_2. Moreover, we bring examples of formulas witnessing SOP_3, and SOP_n for all n greater than or equal to 2