An Observation regarding 0,1-laws and Asymptotics of Definable Sets in Geometric Fraïssé Classes
نویسنده
چکیده
We examine one consequence for the generic theory TC of a geometric Fraïssé C when C has the 0,1-law for first-order logic with convergence to TC itself. We show that in this scenario, if the asymptotic probability measure in play is not terribly exotic, then C is “very close” to being a 1-dimensional asymptotic class – so that TC is super-simple of finite SU -rank.
منابع مشابه
Remarks on almost-sure theories of Fraïssé classes
In addition to demonstrations that certain concrete classes have 0,1-laws, there are a few general sufficient conditions now known guaranteeing that an א0-categorical theory is the almost-sure theory of some Fraïssé class – for example [3] and [16]. In this paper, we work on the converse project: determining what almost-sure theories must be like. We prove two theorems within this project. In t...
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We examine one consequence for the generic theory TC of a geometric Fräıssé class C when C has the 0, 1-law for first-order logic with convergence to TC itself. We show that in this scenario, if the asymptotic probability measure in play is not terribly exotic, then C is “very close” to being a 1-dimensional asymptotic class—so that TC is supersimple of finite SU -rank. Introduction. In much of...
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