An element of a finitely generated non-Abelian free group F (X) is said to be filling if that element has positive translation length in every very small minimal isometric action of F (X) on an R-tree. We give a proof that the set of filling elements of F (X) is exponentially F (X)-generic in the sense of Arzhantseva and Ol’shanskĭı. We also provide an algebraic sufficient condition for an elem...

When presented with a small set of sample objects, human observers have the striking capacity to induce a more general class. Generalization can even proceed from a single object ("one-shot categorization"). The inference is apparently guided by the principle that a good categorical hypothesis is one in which the observed object would be a typcal, "non-accidental," or generic example; this idea...

For a compact metric space ∆ we consider the compact space S(∆) of shift-invariant subsystems of the full shift ∆, endowed with the Hausdorf metric.. We show that when ∆ is perfect the space S(∆) and the homeomorphism group Homeo(K) of the Cantor set (with the topology of uniform convergence) are topologically generically equivalent in the sense of Glasner and King [7], ie a dynamical property ...

Fact. If R is generic over L then for some L-amenable class A, Sat〈L,A〉 is not definable over 〈L[R], A〉, where Sat〈L,A〉 is the canonical satisfaction predicate for 〈L,A〉. Thus Theorem A is established by producing a real R s.t. O / ∈ L[R] yet Sat〈L,A〉 is definable over 〈L[R], A〉 for each L-amenable A. A weaker version of the Genericity Conjecture would state: If O / ∈ L[R] then either R ∈ L or ...

This paper presents a simple generalization of the basic atomic read/write register object, whose genericity parameter spans the whole set of integers and is such that its k-parameterized instance has exactly consensus number k. This object, whose definition is pretty natural, is a sliding window register of size k. Its interest lies in its simplicity and its genericity dimension which provides...