Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCM-trivial structures without the canonical base property
188
0
0.0
(
0
)
Authors
Thomas Blossier
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 that do not have the cupping property, which answers a question of Kristiansen, Schlage-Puchta, and Weiermann. In fact, we show that if $mathbf b$ is a sufficiently large honest elementary degree, then there is a non-zero honest elementary degree $mathbf a <_{mathrm E} mathbf b$ that does not cup to $mathbf b$. For comparison, we modify a result of Cai to show that in sever
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 strictly increasing sequence of characterizable cardinals (Definition 2.1) whose models satisfy JEP$(<lambda_0)$, there is an $L_{omega_1,omega}$ -sentence $psi$ whose models form a pure AEC and (1) The models of $psi$ satisfy JEP$(<lambda_0)$, while JEP fails for all larger cardinals and AP fails in all infinite cardinals. (2) There exist $2^{lambda_i^+}$ non-isomorphic maximal models of $psi$ in $lambda_i^+$, for all $i le alpha$, but no maximal models in any other cardinality; and (3) $psi$ has arbitrarily large models. In particular this shows the Hanf number for JEP and the Hanf number for maximality for pure AEC with Lowenheim number $aleph_0$ are at least $beth_{omega_1}$. We show that although AP$(kappa)$ for each $kappa$ implies the full amalgamation property, JEP$(kappa)$ for each kappa does not imply the full joint embedding property. We show the main combinatorial device of this paper cannot be used to extend the main theorem to a complete sentence.
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 bounded set of Hodge numbers in any given dimension, even as the codimension is allowed to grow.
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 interpreted as assertions that particular matrices are partition regular. In the finite case, Rado proved that a matrix is partition regular if and only it satisfies a computable condition known as the columns property. The first requirement of the columns property is that some set of columns sums to zero. In the infinite case, much less is known. There are many examples of matrices with the columns property that are not partition regular, but until now all known examples of partition regular matrices did have the columns property. Our main aim in this paper is to show that, perhaps surprisingly, there are infinite partition regular matrices without the columns property --- in fact, having no set of columns summing to zero. We also make a conjecture that if a partition regular matrix (say with integer coefficients) has bounded row sums then it must have the columns property, and prove a first step towards this.
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 function ${bf T}_{k,sigma}^{[4]}(z)= sum_n{sf T}_{k,sigma}^{[4]}(n)z^n$ and derive the asymptotic formulas ${sf T}_{k,3}^{[4]}(n)^{}sim c_k n^{-(k-1)^2-frac{k-1}{2}} (gamma_{k,3}^{[4]})^{-n}$ for $k=3,...,9$. In particular we have for $k=3$, ${sf T}_{3,3}^{[4]}(n)^{}sim c_3 n^{-5} 2.0348^n$. Our results prove that the set of biophysically relevant RNA pseudoknot structures is surprisingly small and suggest a new structure class as target for prediction algorithms.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
