Understanding input effects is crucial for delineating the roles of Universal Grammar and learning in grammatical development. Unlike the input effects seen in vocabulary development (Huttenlocher, Haight, Bryk, Seltzer, & Lyons, 1991; Hart & Risley, 1995), effects on grammatical development have been more difficult to identify (Newport, Gleitman, & Gleitman, 1977; Hoff-Ginsberg, 1998; Huttenlo...

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N , m, and prime p with p not dividing N , there is only...

Let H be a Krull monoid with infinite cyclic class group G and let GP ⊂ G denote the set of classes containing prime divisors. We study under which conditions on GP some of the main finiteness properties of factorization theory—such as local tameness, the finiteness and rationality of the elasticity, the structure theorem for sets of lengths, the finiteness of the catenary degree, and the exist...

certain algebraic invariants of the integral group ring zg of a group g were introduced and investigated in relation to the problem of extending the farrell-tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. it turns out that the finiteness of these invariants of a group g implies the existence of a generalized farrell-tate cohomology for g whic...