Geodesic
On 0, 1-laws and asymptotics of definable sets in geometric Fraïssé classes
Cameron Donnay Hill1
1 Department of Mathematics and Computer Science Wesleyan University 655 Exley Science Tower 265 Church Street Middletown, CT 06459, U.S.A.
Fundamenta Mathematicae, Tome 239 (2017) no. 3, pp. 201-219

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm122-1-2017
Keywords: examine consequence generic theory mathbf geometric fra class mathbf mathbf has law first order logic convergence mathbf itself scenario asymptotic probability measure play terribly exotic mathbf close being dimensional asymptotic class mathbf supersimple finite su rank

Cameron Donnay Hill 1

1 Department of Mathematics and Computer Science Wesleyan University 655 Exley Science Tower 265 Church Street Middletown, CT 06459, U.S.A. 
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Cameron Donnay Hill. On 0, 1-laws and asymptotics of definable sets in geometric Fraïssé classes. Fundamenta Mathematicae, Tome 239 (2017) no. 3, pp. 201-219. doi: 10.4064/fm122-1-2017

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