2020/01/02 by Omer Mermelstein, Mermelstein, Omer
Mathematics · #03C13 #03C30 (Primary) 03C45 #03C50 (Secondary) #05B35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #math.CO #math.LO #msc:03C13 #msc:03C30 #msc:03C45 #msc:03C50 #msc:05B35
paper · pdf · doi:10.48550/arxiv.2001.00609
openalex publication_date 2020/01/02 · arxiv created 2020/06/03 · arxiv updated 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine the first order structure of pregeometries of structures built via Hrushovski constructions. In particular, we show that the class of flat pregeometries is an amalgamation class such that the pregeometry of the unbounded arity Hrushovski construction is precisely its generic. We show that the generic is saturated, provide an axiomatization for its theory, show that the theory is ω-stable, and has quantifier-elimination down to boolean combinations of ∃∀-formulas. We show that the pregeometries of the bounded-arity Hrushovski constructions satisfy the same theory, and that they in fact form an elementary chain.