¿En qué consiste el método para construir modelos de la Teoría de conjuntos llamado “FORCING” que creó Cohen (1963-64) ? y ¿Cuál es su importancia en las Matemáticas contemporáneas?. “No es fácil explicar los detalles del trabajo de Cohen en pocas palabras y a no especialistas en lógica”.

Toda buena familia que se precie cuenta, al menos, con un pariente maldito: ese tío, primo o hermano cuya existencia se prefiere pasar por alto, y al que todos se refieren de tapadillo, como si su sola mención bastase para conjurar una presencia intempestiva. Entre la familia de los pensadores del siglo XX, pocos miembros tan intempestivos ha habido como Oswald Spengler. Y no será por falta de éxito, o por la escasa repercusión de su obra. En los años posteriores a la primera guerra mundial su obra principal – La decadencia de Occidente – vendió miles de ejemplares y encendió considerables polémicas, catapultándole a la fama como autor de uno de los mayores best seller filosóficos de todos los tiempos. Pero el éxito no implica la aquiescencia: Spengler concitó en sus obras la enemistad de casi todas las corrientes ideológicas de la época: liberales, cristianos, socialdemócratas, nazis y bolcheviques. No está nada mal

The aim of this paper is to introduce the notion of fantastic deductive systems on generalizations of fuzzy structures, and to emphasize their role in the probability theory on these algebras. We give a characterization of commutative pseudo-BE algebras and we generalize an axiom system consisting of four identities to the case of commutative pseudo-BE algebras. We define the fantastic deductive systems of pseudo-BE algebras and we investigate their properties. It is proved that, if a pseudo-BE(A) algebra A is commutative, then all deductive systems of A are fantastic. Moreover, we generalize the notions of measures, state-measures and measure-morphisms to the case of pseudo-BE algebras and we also prove that there is a one-to-one correspondence between the set of all Bosbach states on a bounded pseudo-BE algebra and the set of its state-measures.

There are so many Daseins as peoples and cultures. And all of them are quite original. We can not compare them because there is no common measure. Each “Dasein” has its own measure – its own concept of time, space, man, God, nature and so on. Serbian “Dasein” we could grasp by Serbian culture by Pavic, by Milic of Machva, by Serbian dances and music, by Serbian history (or rather by the historical – Seynsgeschichtliche). Each people has its own manner to die. And Serbian manner is heroic and profoundly Christian, exemplified by Vidovdan.

This is the introduction I wrote for the multi-authored book “From Riemann to differential geometry and relativity”, edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters, written by various authors. This introduction, besides giving the information on the content of the book, is a quick review of the topics on which Riemann worked and of the impact of this work on mathematics (topology, complex geometry, algebraic geometry, integration, trigonometric series, Riemannian geometry, etc.), philosophy and physics.

It is shown that the boldface maximality principle for subcomplete forcing, together with the assumption that the universe has only set-many grounds, implies the existence of a (parameter-free) definable well-ordering of P(ω 1 ) . The same conclusion follows from the boldface maximality for subcomplete forcing, assuming there is no inner model with an inaccessible limit of measurable cardinals. Similarly, the bounded subcomplete forcing axiom, together with the assumption that x # does not exist, for some x⊆ω 1 , implies the existence of a well-order of P(ω 1 ) which is Δ 1 -definable without parameters, and Δ 1 (H ω 2 ) -definable using a subset of ω 1 as a parameter. This well-order is in L(P(ω 1 )) .

We assume that a voter’s judgment about a proposal depends on (i) the proposal’s probability of being right (or good or just) and (ii) the voter’s probability of making a correct judgment about its rightness (or wrongness). Initially, the state of a proposal (right or wrong), and the correctness of a voter’s judgment about it, are assumed to be independent. If the average probability that voters are correct in their judgments is greater than ½, then the proposal with the greatest probability of being right will, in expectation, receive the greatest number of approval votes. This result holds, as well, when the voters’ probabilities of being correct depend on the state of the proposal; when the average probability that voters judge a proposal correctly is functionally related to the probability that it is right, provided that the function satisfies certain conditions; and when all voters follow a leader with an above-average probability of correctly judging proposals. However, it is possible that voters may more frequently select the proposal with the greatest probability of being right by reporting their independent judgments—as assumed by the Condorcet Jury Theorem—rather than by following any leader. Applications of these results to different kinds of voting situations are discussed.

A partir del examen de la noción de dialéctica ofrecida por Jean-Paul Sartre en “Cuestiones de método”, se identifican tres características propias de dicha noción presentes en la dialéctica de Hegel: el papel de la reflexión, la negatividad y la relación entre la dialéctica y la subjetividad.

In the paper, the idea of describing not-yet-verified (i.e., pre-existing) properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea one must first decide how to deal with bivalence of the everyday macrophysical experience in many-valued semantics and, correspondingly, clear up the tradeoff between logical 2-valuedness and many-valuedness. The conceptual difficulties accompanying a two-valued reduction of many-valued logics are discussed.

The global energy system is undergoing a major transition, and in energy planning and decision-making across governments, industry and academia, models play a crucial role. Because of their policy relevance and contested nature, the transparency and open availability of energy models and data are of particular importance. Here we provide a practical how-to guide based on the collective experience of members of the Open Energy Modelling Initiative (Openmod). We discuss key steps to consider when opening code and data, including determining intellectual property ownership, choosing a licence and appropriate modelling languages, distributing code and data, and providing support and building communities. After illustrating these decisions with examples and lessons learned from the community, we conclude that even though individual researchers’ choices are important, institutional changes are still also necessary for more openness and transparency in energy research.