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  1. Pubblicazioni

STRONGLY MINIMAL STEINER SYSTEMS I: EXISTENCE

Articolo
Data di Pubblicazione:
2021
Abstract:
A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner k-system (for k > 2) is a linear space such that each line has size exactly k. Clearly, as a two-sorted structure, no linear space can be strongly minimal. We formulate linear spaces in a (bi-interpretable) vocabulary z with a single ternary relation R. We prove that for every integer k there exist 2.1 -many integer valued functions g such that each g determines a distinct strongly minimal Steiner k-system ci, whose algebraic closure geometry has all the properties of the ab initio Hrushovski construction. Thus each is a counterexample to the Zilber Trichotomy Conjecture.
Tipologia CRIS:
03A-Articolo su Rivista
Keywords:
strongly minimal; Steiner system; Hrushovski construction
Elenco autori:
Baldwin, J; Paolini, G
Autori di Ateneo:
PAOLINI Gianluca
Link alla scheda completa:
https://iris.unito.it/handle/2318/1837544
Pubblicato in:
THE JOURNAL OF SYMBOLIC LOGIC
Journal
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