Relatively computably enumerable reals

A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and Y does not compute X. A real X is relatively simple and above if there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset Z of the complement of X such that Z is c.e.(Y). We prove that every nonempty Pi^0_1 class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above.Comment: 5 pages. Significant changes from earlier versio

Genericity and measure for exponential time

AbstractRecently, Lutz [14, 15] introduced a polynomial time bounded version of Lebesgue measure. He and others (see e.g. [11, 13–18, 20]) used this concept to investigate the quantitative structure of Exponential Time (E = DTIME(2lin)). Previously, Ambos-Spies et al. [2, 3] introduced polynomial time bounded genericity concepts and used them for the investigation of structural properties of NP (under appropriate assumptions) and E. Here we relate these concepts to each other. We show that, for any c ⩾ 1, the class of nc-generic sets has p-measure 1. This allows us to simplify and extend certain p-measure 1-results. To illustrate the power of generic sets we take the Small Span Theorem of Juedes and Lutz [11] as an example and prove a generalization for bounded query reductions

¿Castigo sin soberano? La cuestión del ius puniendi en derecho penal internacional Una primera contribución para una teoría del derecho penal internacional consistente

El derecho penal internacional actual (“DPI”) adolece de cuatro graves defectos. Primero, es preciso clarificar su concepto y significado. Segundo, ha de resolverse la cuestión de si y cómo puede existir el poder punitivo a nivel supranacional sin un soberano. Tercero, hay que explicar mejor su función o propósito global, por oposición a los del derecho penal nacional. Cuarto, se deben desarrollar los fines de la pena en el DPI, por oposición a los fines tradicionales del derecho penal nacional. Estas cuestiones se relacionan en parte vertical y en parte horizontalmente. Así, es imposible reflexionar sobre el ius puniendi, sobre la función global y sobre los fines de la pena sin haber clarificado primero el concepto de DPI. Además, un tratamiento de su función y de los fines de la pena tiene que basarse en la justificación del ius puniendi siendo así que, la falta de una respuesta satisfactoria a esta cuestión es, quizás, la debilidad teórica más importante del DPI actual. Este trabajo pretende demostrar que el ius puniendi supranacional puede ser inferido de una combinación del incipiente carácter supranacional del orden mundial (entendido como un orden de valores) con el concepto de una sociedad mundial compuesta por ciudadanos del mundo, cuyo derecho (‘Weltbürgerrecht’) se deriva de derechos humanos universales, indivisibles y reconocidos interculturalmente, fundados en un concepto kantiano de dignidad humana. Ambos son representados por la comunidad internacional (comunidad de valores) que es así el titular del ius puniendi

Just war and military morale: a brief reflection on the correlation between the legality of war and the moral repercussions for members of US and UK forces arising from the questionable legality of the campaign Iraqi Freedom of March 2003

Does it matter to a member of the military whether the military campaign in which he is taking part is lawful or not? Despite the observation that the crime of aggression (post Kampala 2010) constitutes a ‘leadership crime par excellence,’ which limits any (future) criminal responsibility accordingly, the legality or illegality of any military action under international law can create moral implications for the common foot soldier and mid-level officer and also have a tangible impact on the national legal frameworks under which these forces operate. This short article uses the example of Operation Iraqi Freedom (2003) to discuss the repercussions of a—most likely—illegal military campaign for individual members of democratic armed forces before the background of the present discussion of NATO led action in Libya

Computable randomness is about more than probabilities

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer

A note on the differences of computably enumerable reals

We show that given any non-computable left-c.e. real α there exists a left-c.e. real β such that α≠β+γ for all left-c.e. reals and all right-c.e. reals γ. The proof is non-uniform, the dichotomy being whether the given real α is Martin-Loef random or not. It follows that given any universal machine U, there is another universal machine V such that the halting probability of U is not a translation of the halting probability of V by a left-c.e. real. We do not know if there is a uniform proof of this fact