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On 0, 1-laws and asymptotics of definable sets in geometric Fraïssé classes

Volume 239 / 2017

Cameron Donnay Hill Fundamenta Mathematicae 239 (2017), 201-219 MSC: 03C13, 03C15, 03C45, 05A16. DOI: 10.4064/fm122-1-2017 Published online: 23 June 2017

Abstract

We examine one consequence for the generic theory $T_\mathbf {C}$ of a geometric Fraïssé class $\mathbf {C}$ when $\mathbf {C}$ has the $0,1$-law for first-order logic with convergence to $T_\mathbf {C}$ itself. We show that in this scenario, if the asymptotic probability measure in play is not terribly exotic, then $\mathbf {C}$ is “very close” to being a 1-dimensional asymptotic class—so that $T_\mathbf {C}$ is supersimple of finite $SU$-rank.

Authors

  • Cameron Donnay HillDepartment of Mathematics and Computer Science
    Wesleyan University
    655 Exley Science Tower
    265 Church Street
    Middletown, CT 06459, U.S.A.
    e-mail

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