We modify the definition of robust chains from [25] as an approach to formalizing the Finite Sub-model Property (see [21], for example) from the perspective of a class of finite structures with a generic model (i.e. having the Amalgamation and Joint-embedding properties). We characterize this formulation, which we call super-robustness, modulo a weaker condition (that is closer to the the situa...

The algebraicity conjecture for simple groups of finite Morley rank, also known as the Cherlin-Zilber conjecture, states that simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields. In the last 15 years, the main line of attack on this problem has been Borovik’s program of transferring methods from finite group theory. Borovik’s program has led to consi...

For analyzing impartial games played in the misère rule, Yamasaki defined flatness of games, while Conway defined tameness. In this paper, we prove that these two concepts are equivalent.

This note surveys basic topological properties of nonarchimedean analytic spaces, in the sense of Berkovich, including the recent tameness results of Hrushovski and Loeser. We also discuss interactions between the topology of nonarchimedean analytic spaces and classical algebraic geometry.

We study various notions of “tameness” for definably complete expansions of ordered fields. We mainly study structures with locally o-minimal open core, d-minimal structures, and dense pairs of d-minimal structures.

The semidirect product of pseudovarieties of semigroups with an order-computable pseudovariety is investigated. The essential tool is the natural representation of the corresponding relatively free profinite semigroups and how it transforms implicit signatures. Several results concerning the behavior of the operation with respect to various kinds of tameness properties are obtained as applicati...

We give an account of the tameness theorem for complete hyperbolic 3-manifolds. Our presentation makes use of ideas from a number of different sources. We aim to give an account that is readily accessible from fairly standard geometrical and topological arguments, and adaptable to variable curvature. Let M be a complete hyperbolic 3-manifold with π1(M) finitely generated. Marden [Ma] asked if t...