Purpose—Clinical grammar markers are needed for children with SLI older than 8 years. This study followed children studied earlier on sentences with omitted finiteness to determine if affected children continue to perform at low levels and to examine possible predictors of low performance. This is the first longitudinal report of grammaticality judgments of questions. Method—Three groups of chi...

A finite rewriting system is presented that does not satisfy the homotopical finiteness condition FDT, although it satisfies the homological finiteness condition FHT. This system is obtained from a group G and a finitely generated subgroup H of G through a monoid extension that is almost an HNN-extension. The FHT property of the extension is closely related to the FP2 property for the subgroup ...

Inspired by Stark’s analytic proof of the finiteness of the class number of a ring of integers in an algebraic number field, we give a new proof of the finiteness of the number of classes of ideals in a maximal order of a quaternion division algebra over a totally real number field. Previous proofs of this well-known result have used adeles or geometry of numbers, while our proof uses the class...

We consider the factorization (collapse) of infinite transition graphs wrt. bisimulation equivalence. It turns out that almost none of the more complex classes of the process taxonomy, which has been established in the last years, are preserved by this operation. However, for the class of BPA graphs (i.e. prefix transition graphs of context-free grammars) we can show that the factorization is e...

We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersections of subgroups and the preservation of finiteness conditions in a uniform manner. We then establish easily the theorems of Greibach and...

In this paper, we continue a study of simplicial commutative algebras with finite André-Quillen homology, that was begun in [19]. Here we restrict our focus to simplicial algebras having characteristic 2. Our aim is to find a generalization of the main theorem in [19]. In particular, we replace the finiteness condition on homotopy with a weaker condition expressed in terms of nilpotency for the...

We introduce acyclic polygraphs, a notion of complete categorical cellular model for (small) categories, containing generators, relations and higher-dimensional globular syzygies. We give a rewriting method to construct explicit acyclic polygraphs from convergent presentations. For that, we introduce higher-dimensional normalisation strategies, defined as homotopically coherent ways to relate e...

We consider locally finite geometries of rank 3 belonging to certain diagrams where all strokes represent classes of non-trivial designs, at least one of them consisting of symmetric designs other than projective planes. The gonality diagram of such geometry is of spherical type, whereas the diameter diagram is of affine type. In cases like this, the criteria available from 24 cannot tell us an...

In three spacetime dimensions, where no graviton propagates, pure gravity is known to be finite. It is natural to ask if finiteness survives the coupling with matter. Standard arguments do not ensure finiteness, but only that there exists a subtraction scheme where no Lorentz-Chern-Simons term is generated by radiative corrections. I consider gravity coupled with Chern-Simons U(1) gauge theory ...

In the folklore of linear logic, a common intuition is that the structure of finiteness spaces, introduced by Ehrhard, semantically reflects the strong normalization property of cut-elimination. We make this intuition formal in the context of the non-deterministic λ-calculus by introducing a finiteness structure on resource terms, which is such that a λ-term is strongly normalizing iff the supp...