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Based on Hrushovski, Palac{i}n and Pillays example [6], we produce a new structure without the canonical base property, which is interpretable in Baudischs group. Said structure is, in particular, CM-trivial, and thus at the lowest possible level of the ample hierarchy.
An element $a$ of a lattice cups to an element $b > a$ if there is a $c < b$ such that $a cup c = b$. An element of a lattice has the cupping property if it cups to every element above it. We prove that there are non-zero honest elementary degrees th
We introduce the notion of a `pure` Abstract Elementary Class to block trivial counterexamples. We study classes of models of bipartite graphs and show: Main Theorem (cf. Theorem 3.5.2 and Corollary 3.5.6): If $(lambda_i : i le alpha<aleph_1)$ is a
We prove birational boundedness results on complete intersections with trivial canonical class of base point free divisors in (some version of) Fano varieties. Our results imply in particular that Batyrev-Borisov toric construction produces only a bo
A finite or infinite matrix A with rational entries is called partition regular if whenever the natural numbers are finitely coloured there is a monochromatic vector x with Ax=0. Many of the classical theorems of Ramsey Theory may naturally be interp
In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $ge 4$. Let ${sf T}_{k,sigma}^{[4]} (n)$ denote the number of these structures. We derive exact enumeration results by computing the generating functi