Submission date: 26 February

Abstract:

The first part of the paper presents the ideas underlying Hrushovski's amalgamation construction in standard geometric stability theoretic terms. The focus is on the part of the construction known as "the collapse", tracing its origins to Zilber's envelopes, Lachlan's "shrinking and stretching" and the Cherlin-Hrushovski smoothly approximable structures. The second part suggests a list of problems (some old) exploring the question of whether Hrushovski's construction technique can be reconciled with an eventual classification of strongly minimal geometries.

Mathematics Subject Classification: 03C45

Keywords and phrases: Amalgamation constructions, strongly minimal sets, regular types, pregeometries, smooth approximations

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