On 0, 1-laws and asymptotics of definable sets in geometric Fraïssé classes
Tom 239 / 2017
Fundamenta Mathematicae 239 (2017), 201-219
MSC: 03C13, 03C15, 03C45, 05A16.
DOI: 10.4064/fm122-1-2017
Opublikowany online: 23 June 2017
Streszczenie
We examine one consequence for the generic theory 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.
