We introduce a general framework to prove undecidability of fragments. This is applied to fragments of theories arising in algebra and recursion theory. For instance, the V3V-theories of the class of finite distributive lattices and of the p.o. of recursively enumerable many-one degrees are shown to be undecidable.

The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favourable for fast simulations and follow-up applications. We present systematic techniques that reduce the grid size while preserving basic functionality in the reduc...

Downey and Lempp 8] have shown that the contiguous computably enumerable (c.e.) degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degre...

We give a rst-order coding without parameters of a copy of (N;+;) in the computably enumerable weak truth table degrees. As a tool,we develop a theory of parameter deenable subsets. Given a degree structure from computability theory, once the undecidability of its theory is known, an important further problem is the question of the actual complexity of the theory. If the structure is arithmetic...

We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of FelixKlein’sErlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and theMartin Invariance Conjecture on their Tur...

The main topic of the present work is the relation that a set X is strongly hyperimmune-free (shif) relative to Y . Here X is shif-below Y if and only if for every partial X-recursive function p there is a partial Y -recursive function q such that every a in the domain of p is also in the domain of q and satisfies p(a) < p(q). It is shown that between degrees not above the halting problem this ...

Introduction. These notes are based on E. L. Post's paper Recursively enumerable sets of positive integers and their decision problems1 to which we shall refer as RES. The reader is assumed to be familiar with §§1-5 and 9 of this paper. In the first note we shall discuss some algebraic properties of simple and hypersimple sets. In the second note we shall prove the existence of a recursively en...

The Red-Sequence Cluster Survey (RCS) is a new galaxy cluster survey designed to provide a large sample of optically selected 0.1<z<1.4 clusters. The planned survey data are 100 square degrees of two color (R and z) imaging, with a 5σ depth ∼2 mag past M at z = 1. The combined depth and area of the RCS make it the widest field, moderately deep survey ever undertaken using 4m class telescopes. T...

Holomorphic differential forms play an important role in the global study of complex projective or compact Kähler manifolds. Forms of degree 1 are well understood: there is a universal map, the Albanese map, to a complex torus and every 1-form is a pull-back. Forms of top degree also play a special role because they are sections in a line bundle, the canonical bundle. Forms of degree d with 2 ≤...

The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or Marsden–Weinstein reduction procedure takes advantage of this and associates to the original system a new Hamiltonian system with fewer degrees of freedom. Howev...