Interpreting groups and fields in simple, finitary AECs

Interpreting groups and fields in simple, finitary AECs

We prove a version of Hrushovski's 1989 results on almost orthogonal regular types in the context of simple and superstable nitary abstract elementary classes: from a certain expression of `non-orthogonality' we can conclude the existence of a group acting on the geometry obtained on the set of realizations of a regular Lascar strong type, and if we rule out the presence of a non-classical grou...

Finitary Permutation Groups

A finitary permutation group is a natural generalization of a finite permutation group. The structure of a transitive finitary permutation group is surprisingly simple when its degree is infinite. Here we study primitivity, following P. M. Neumann’s work in the 1970s. We also study generalized solubility conditions on these groups. These notes arose from lectures aimed at an audience who had se...

Interpreting a Finitary Pi-calculus in Differential Interaction Nets

homogenous finitary symmetric groups

we characterize strictly diagonal type of embeddings offinitary symmetric groups in terms of cardinality and the characteristic. namely, we prove thefollowing.let $kappa$ be an infinite cardinal. if$g=underset{i=1}{stackrel{infty}bigcup} g_i,$ where $ g_i=fsym(kappa n_i)$,$(h=underset{i=1}{stackrel{infty}bigcup}h_i, $ where $ h_i=alt(kappa n_i) ), $ is a group of strictly diagonal type and$xi=(...

Model Theory of Finite Difference Fields and Simple Groups

Asymptotic classes are classes of finite structures which have uniformly definable estimates for the cardinalities of their first-order definable sets akin to those in finite fields given by the Lang-Weil estimates. The goal of the thesis is to prove that the finite simple groups of a fixed Lie type and Lie rank form asymptotic classes. This requires the following: 1. The introduction describes...