An empty inverse limit

Behavioural Inverse Limit λ-Models

We construct two inverse limit λ-models which completely characterise sets of terms with similar computational behaviours: the sets of normalising, head normalising, weak head normalising λ-terms, those corresponding to the persistent versions of these notions, and the sets of closable, closable normalising, and closable head normalising λ-terms. More precisely, for each of these sets of terms ...

Every Module Is an Inverse Limit of Injectives

It is shown that any left module A over a ring R can be written as the intersection of a downward directed system of injective submodules of an injective module; equivalently, as an inverse limit of one-to-one homomorphisms of injectives. If R is left Noetherian, A can also be written as the inverse limit of a system of surjective homomorphisms of injectives. Some questions are raised. The flat...

An Inverse Limit of Context-Free Grammars - A New Approach to Identifiability in the Limit

An Empty Revolution

On December 2, when Venezuelans delivered President Hugo Chávez his first electoral defeat in nine years, most analysts were taken by surprise. According to o⁄cial results, 50.7 percent of voters rejected Chávez’s proposed constitutional reform, which would have expanded executive power, gotten rid of presidential term limits, and paved the way for the construction of a “socialist” economy. It ...

Inverse limit of M-cocycles and applications

For any m, 2 ≤ m <∞, we construct an ergodic dynamical system having spectral multiplicity m and infinite rank. Given r > 1, 0 < b < 1 such that rb > 1 we construct a dynamical system (X,B, μ, T ) with simple spectrum such that r(T ) = r, F ∗(T ) = b, and #C(T )/wcl{Tn : n ∈ Z} =∞.