ABSTRACTWe introduce the variety of Many-Valued-Weak rigs. We provide an axiomatisation and establish, in this context, basic properties about ideals, homomorphisms, quotients and radicals. This new class contains the class of product MV-algebras presented by Di Nola and Dvurečenskij in 2001 and by Montagna in 2005. The main result is the compactness of the prime spectrum of this new class, endowed with the co-Zariski topology as defined by Dubuc and Poveda in 2010.

In this paper, we provide a set-theoretic proof of the general representation theorem for MV-algebras, which was developed by Dubuc and Poveda in 2010. The theorem states that every MV-algebra is isomorphic to the MV-algebra of all global sections of its prime spectrum. We avoid using topos theory and instead rely on basic concepts from MV-algebras, topology and set theory.

In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class of notions of forcing which we call [Formula: see text]-Prikry, and showed that many of the known Prikry-type notions of forcing that center around singular cardinals of countable cofinality are [Formula: see text]-Prikry. We showed that given a [Formula: see text]-Prikry poset [Formula: see text] and a [Formula: see text]-name for a (...) non-reflecting stationary set [Formula: see text], there exists a corresponding [Formula: see text]-Prikry poset that projects to [Formula: see text] and kills the stationarity of [Formula: see text]. In this paper, we develop a general scheme for iterating [Formula: see text]-Prikry posets and, as an application, we blow up the power of a countable limit of Laver-indestructible supercompact cardinals, and then iteratively kill all non-reflecting stationary subsets of its successor. This yields a model in which the singular cardinal hypothesis fails and simultaneous reflection of finite families of stationary sets holds. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class of notions of forcing which we call [math]-Prikry, and showed that many of the known Prikry-type notions of forcing that center around singular cardinals of countable cofinality are [math]-Prikry. We showed that given a [math]-Prikry poset [math] and a [math]-name for a (...) non-reflecting stationary set [math], there exists a corresponding [math]-Prikry poset that projects to [math] and kills the stationarity of [math]. In this paper, we develop a general scheme for iterating [math]-Prikry posets and, as an application, we blow up the power of a countable limit of Laver-indestructible supercompact cardinals, and then iteratively kill all non-reflecting stationary subsets of its successor. This yields a model in which the singular cardinal hypothesis fails and simultaneous reflection of finite families of stationary sets holds. (shrink)

The dissertation under comment is a contribution to the area of Set Theory concerned with the interactions between the method of Forcing and the so-called Large Cardinal axioms.The dissertation is divided into two thematic blocks. In Block I we analyze the large-cardinal hierarchy between the first supercompact cardinal and Vopěnka’s Principle. In turn, Block II is devoted to the investigation of some problems arising from Singular Cardinal Combinatorics.We commence Part I by investigating the Identity Crisis phenomenon in the region comprised (...) between the first supercompact cardinal and Vopěnka’s Principle. As a result, we generalize Magidor’s classical theorems [2] to this higher region of the large-cardinal hierarchy. Also, our analysis allows to settle all the questions that were left open in [1]. Finally, we conclude Part I by presenting a general theory of preservation of $C^{}$ -extendible cardinals under class forcing iterations. From this analysis we derive several applications. For instance, our arguments are used to show that an extendible cardinal is consistent with “ $^{\mathrm {HOD}}<\lambda ^+$, for every regular cardinal $\lambda $.” In particular, if Woodin’s HOD Conjecture holds, and therefore it is provable in ZFC + “There exists an extendible cardinal” that above the first extendible cardinal every singular cardinal $\lambda $ is singular in HOD and $^{\textrm {{HOD}}}=\lambda ^+$, there may still be no agreement at all between V and HOD about successors of regular cardinals.In Part II and Part III we analyse the relationship between the Singular Cardinal Hypothesis with other relevant combinatorial principles at the level of successors of singular cardinals. Two of these are the Tree Property and the Reflection of Stationary sets, which are central in Infinite Combinatorics.Specifically, Part II is devoted to prove the consistency of the Tree Property at both $\kappa ^+$ and $\kappa ^{++}$, whenever $\kappa $ is a strong limit singular cardinal witnessing an arbitrary failure of the SCH. This generalizes the main result of [3] in two senses: it allows arbitrary cofinalities for $\kappa $ and arbitrary failures for the SCH.In the last part of the dissertation we introduce the notion of $\Sigma $ -Prikry forcing. This new concept allows an abstract and uniform approach to the theory of Prikry-type forcings and encompasses several classical examples of Prikry-type forcing notions, such as the classical Prikry forcing, the Gitik-Sharon poset, or the Extender Based Prikry forcing, among many others.Our motivation in this part of the dissertation is to prove an iteration theorem at the level of the successor of a singular cardinal. Specifically, we aim for a theorem asserting that every $\kappa ^{++}$ -length iteration with support of size $\leq \kappa $ has the $\kappa ^{++}$ -cc, provided the iterates belong to a relevant class of $\kappa ^{++}$ -cc forcings. While there are a myriad of works on this vein for regular cardinals, this contrasts with the dearth of investigations in the parallel context of singular cardinals. Our main contribution is the proof that such a result is available whenever the class of forcings under consideration is the family of $\Sigma $ -Prikry forcings. Finally, and as an application, we prove that it is consistent—modulo large cardinals—the existence of a strong limit cardinal $\kappa $ with countable cofinality such that $\mathrm {SCH}_\kappa $ fails and every finite family of stationary subsets of $\kappa ^+$ reflects simultaneously. (shrink)

In this paper we study the notion of $C^{}$ -supercompactness introduced by Bagaria in [3] and prove the identity crises phenomenon for such class. Specifically, we show that consistently the least supercompact is strictly below the least $C^{}$ -supercompact but also that the least supercompact is $C^{}$ -supercompact }$ -supercompact). Furthermore, we prove that under suitable hypothesis the ultimate identity crises is also possible. These results solve several questions posed by Bagaria and Tsaprounis.

We prove two general results about the preservation of extendible and $C^{(n)}$ -extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vopěnka’s Principle and $C^{(n)}$ -extendible cardinals under Jensen’s iteration for forcing the GCH [17], previously obtained in [8, 27], respectively. We prove that $C^{(n)}$ -extendible cardinals are preserved by forcing with standard Easton-support iterations for any possible $\Delta _2$ -definable behaviour of the power-set function on (...) regular cardinals. We show that one can force proper class-many disagreements between the universe and HOD with respect to the calculation of successors of regular cardinals, while preserving $C^{(n)}$ -extendible cardinals. We also show, assuming the GCH, that the class forcing iteration of Cummings–Foreman–Magidor for forcing $\diamondsuit _{\kappa ^+}^+$ at every $\kappa $ [10] preserves $C^{(n)}$ -extendible cardinals. We give an optimal result on the consistency of weak square principles and $C^{(n)}$ -extendible cardinals. In the last section prove another preservation result for $C^{(n)}$ -extendible cardinals under very general (not necessarily definable or weakly homogeneous) class forcing iterations. As applications we prove the consistency of $C^{(n)}$ -extendible cardinals with $\mathrm {{V}}=\mathrm {{HOD}}$, and also with $\mathrm {GA}$ (the Ground Axiom) plus $\mathrm {V}\neq \mathrm {HOD}$, the latter being a strengthening of a result from [14]. (shrink)

We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Theorem 2.3].

An action research project was carried out, using theater workshops and basic digital fabrication technology workshops to improve social skills—such as the expression of emotions, communication, self-control, and teamwork—in a group of 10 young individuals with autism spectrum disorder. This article focuses on the digital fabrication workshops, where participants worked on the fundamentals of electronics and programming, as well as 3D design and printing, to make props that were later used on stage in the theatrical performances in which they participated. (...) These workshops were systematized through observation guides. According to the results, it was evident that the participants not only enjoyed and gained technological knowledge, but that their social skill development needs were addressed. Professionals from the Special Education Faculty and the Fab Lab Kä Träre, both from Universidad Estatal a Distancia in Costa Rica, were in charge of the study during its first phase, executed in 2016 and 2017. (shrink)

En este trabajo, después de contrastar la opinión de Kant y Aristóteles sobre la responsabilidad y la libertad ante la coacción, y tras unas sucintas consideraciones sobre el tema de la libertad en el pensamiento islámico, se pasa revista a lo que sobre la coacción han dicho los pensadores más representativos del área islámica clásica. Estos pensadores son, ante todo, los mutakallimíes, los “teólogos” del islam, distinguiéndose entre ellos un grupo, los muʿtazilíes, que son los que han dado mayor entrada (...) a la razón en sus especulaciones, y entre estos destacan los análisis de ‘Abd al-Jabbâr que es el autor que más se ha ocupado de este asunto. Finalmente se contrasta la opinión de este autor con las de al-Bâqillânî y Algazel, cuya solución es muy próxima a la de Kant. Sigue un breve Apéndice para ilustrar la cuestión tratada a través de las reflexiones de Semprun y Améry sobre su experiencia de la coacción sufrida. (shrink)

This paper critically explores the ethical dimensions of Behavioral Public Policy (BPP), a domain grounded in the understanding that human rationality is bounded and that this limitation often leads to behaviors deemed irrational. By applying the behavioral lens, which posits that people operate under bounded rationality, BPP aims to craft interventions that safeguard individuals against their biases. However, this approach raises significant ethical concerns, both in the scientific underpinnings of BPP and its application through policy interventions. Accordingly, this paper examines (...) two distinct ethical dimensions of BPP, both as a scientific discipline and through its intervention methodologies. The analysis of the first dimension argues that, viewing bounded rationality as only instrumental in decision-making processes, risks oversimplifying ethical complexities. Such simplification may ignore the moral and value-based rationalities underlying decisions, potentially misattributing instances of immorality and akrasia (the failure to act according to one's judgment) to mere deficiencies in rational thinking. Secondly, the paper examines the impact of BPP on moral behavior and character development, addressing ethical concerns like the evidentiary basis of BPP research, the bounded rationality of choice architects themselves, and the morality of behavior changes induced by policy. Overall, this article provides a much-needed examination of the moral considerations associated with behavioral strategies in public policy and its epistemological foundations, contributing to a more comprehensive understanding of their ethical implications . (shrink)

En este artículo analizo la interpretación de Hegel de la filosofía política platónica (particularmente la República) en determinados pasajes de dos obras puntuales: los Fundamentos de la filosofía del derecho y las Lecciones sobre Platón. Considero dos ejes específicos de análisis: la propiedad privada y la libertad subjetiva. El objetivo del artículo es señalar la relación que Hegel establece con Platón o, al menos, con República. Muestro que, en realidad, en este diálogo existen ciertos matices con respecto a los dos (...) ejes mencionados; estos matices implican diferencias de análisis respecto de la lectura hegeliana. (shrink)

The present volume brings together a number of studies, eight in all, dedicated to diverse aspects of Aristotle's conception of rational action and practical rationality. Two principal motifs account for their thematic unity. The first one is given in the idea that Aristotle's view is characterized by a fundamental tension between the totalizing orientation of practical rationality, on the one hand, and the situational subjection of human action, on the other. The second one concerns the connection that Aristotle establishes between (...) rational action (praxis) and truth, expressed in the notion of practical truth. The proposed interpretation seeks to show that Aristotle's conception is not just internally consistent and philosophically interesting; it is also capable of entering into fruitful dialogue with a whole range of modern and contemporary views. (shrink)

It is commonly accepted that Han Fei studied under Xunzi sometime during the late third century BCE. However, there is surprisingly little dedicated to the in-depth study of the relationship between Xunzi’s ideas and one of his best-known followers. In this essay I argue that Han Fei’s notion of xing, commonly translated as human nature, was not only influenced by Xunzi but also that it is an important feature of his political philosophy.

Ensayos-homenaje en el primer centenario del nacimiento del fil sofo espa ol, que abordan diversos aspectos de la obra de Ortega. Los cuatro trabajos dibujan con rigor algunos de los horizontes planteados por el maestro y respetan la debida modernidad conceptual. la compilaci n estuvo a cargo de Fernando Salmer n, Alejandro Rossi, Luis Villoro y Ram n Xirau.

Despite impressive technological developments, there is something that does not seem to have changed in the future of the Alien saga: capitalist society. The capitalist mode of production was largely triggered by an important event in the history of humanity: the Industrial Revolution. In the Alien films the worst tendencies of capitalism seem to drive the Weyland‐Yutani Corporation's decisions, confirming Karl Marx's fears that people would not be at the center of the process of capitalist production. It is clear the (...) Weyland‐Yutani Corporation has taken its goal of acquisition of profit at all costs very seriously, as demonstrated by Special Order 937. Alienation is one of Marx's key ideas. This chapter mainly focuses on alienation as it is described in a series of notebooks written in 1857‐1858, also known as the Grundrisse. Marx concludes, based on insights from ancient Greek and Hellenistic philosophers, that the good life should be one of active self‐realization and autonomy. (shrink)

In the beginning of Star Trek Into Darkness, Mr. Spock descends into the heart of a raging volcano on the planet Nibiru. His mission: to detonate a cold fusion device that will solidify the bubbling magma before it erupts and destroys an entire civilization. Meanwhile, Captain James T. Kirk is on the bridge of the Enterprise facing a dilemma. He's duty‐bound never to violate the Prime Directive. One way to address the problem of the Prime Directive is to follow the (...) criteria used by Vulcans: reason and logic. This approach has been highly revered in the history of moral philosophy, and was most convincingly articulated by Immanuel Kant. Confucius and Aristotle would agree that while the Prime Directive is usually correct, there will be cases where it's wrong not to break it. The Prime Directive symbolizes just how difficult making good moral decisions can be. (shrink)

The literary genesis of Einbahnstraße by Walter Benjamin represents a very special case of the use of the procedures of surrealism in the philosophical-literary production of the author. The process of evolution of thinking that ended up in the writing of this piece is unveiled throughout the present analysis. This is a sign of both waiver and restart; the opening for a new productive dimension in the career of one of the most important —and misunderstood— philosophers of the 20th century. (...) More than enlightening a small master piece of philosophy from a literary perspective, or analyzing a small master piece of literature from the philosophy, what is being problematized here is the division, cultivated or figured throughout the years, between both disciplines. This work is intended to recover what is insoluble from the philosophical-literary labor of Walter Benjamin, besides tracing a possible reconfiguration for an interdisciplinary field of work to come up and contribute in the understanding of the problem called The Retreat of Metaphor by Jacques Derrida. (shrink)

Patagonia: Land of Giants captures the wonders of the Patagonian landscape in hundreds of stunning color photographs by famed Argentine nature photographer Daniel Rivademar.

Indisciplinar el vestigio conlleva retornarle su potencia antimoderna y decolonial. Desde un mero punto de vista epistemológico sería abordar la simultanedidad como apertura al conocimiento, traspasar los umbrales divisorios de la ciencia colonial, conectar lo que la disciplina ha separado y fluir aquello que ha sido estancado. La arqueología es una herramienta fundamental del conocimiento contrahegemónico. Pero, al mismo tiempo, y dado que las relaciones evestigiales son simultáneas, estratificadas y constitutivas tanto del mundo como de nuestra relación en el mundo, (...) el otro lado del vestigio importa mucho más que una apertura al conocimiento. (shrink)

In this essay I revise, based on the notion of the ‘enlightened ruler’ or mingzhu and his critique of the literati of his time, the common belief that Han Fei was an amoralist and an advocate of tyranny. Instead, I will argue that his writings are dedicated to advising those who ought to rule in order to achieve the goal of a peaceful and stable society framed by laws in accordance with the dao.