This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the open and (...) clopen Ramsey theorems. Since there is not a canonical way to phrase these theorems as multi-valued functions, we identify eight different multi-valued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility.We then discuss some new operators on multi-valued functions and study their algebraic properties and the relations with other previously studied operators on problems. In particular, we study the first-order part and the deterministic part of a problem f, capturing the Weihrauch degree of the strongest multi-valued problem that is reducible to f and that, respectively, has codomain $\mathbb {N}$ or is single-valued.These notions proved to be extremely useful when exploring the Weihrauch degree of the problem $\mathsf {DS}$ of computing descending sequences in ill-founded linear orders. They allow us to show that $\mathsf {DS}$, and the Weihrauch equivalent problem $\mathsf {BS}$ of finding bad sequences through non-well quasi-orders, while being very “hard” to solve, are rather weak in terms of uniform computational strength. We then generalize $\mathsf {DS}$ and $\mathsf {BS}$ by considering $\boldsymbol {\Gamma }$ -presented orders, where $\boldsymbol {\Gamma }$ is a Borel pointclass or $\boldsymbol {\Delta }^1_1$, $\boldsymbol {\Sigma }^1_1$, $\boldsymbol {\Pi }^1_1$. We study the obtained $\mathsf {DS}$ -hierarchy and $\mathsf {BS}$ -hierarchy of problems in comparison with the Baire hierarchy and show that they do not collapse at any finite level.Finally, we work in the context of geometric measure theory and we focus on the characterization, from the point of view of descriptive set theory, of some conditions involving the notions of Hausdorff/Fourier dimension and Salem sets. We first work in the hyperspace $\mathbf {K}$ of compact subsets of $[0,1]$ and show that the closed Salem sets form a $\boldsymbol {\Pi }^0_3$ -complete family. This is done by characterizing the complexity of the family of sets having sufficiently large Hausdorff or Fourier dimension. We also show that the complexity does not change if we increase the dimension of the ambient space and work in $\mathbf {K}$. We also generalize the results by relaxing the compactness of the ambient space and show that the closed Salem sets are still $\boldsymbol {\Pi }^0_3$ -complete when we endow $\mathbf {F}$ with the Fell topology. A similar result holds also for the Vietoris topology.We conclude by analyzing the same notions from the point of view of effective descriptive set theory and Type-2 Theory of Effectivity, and show that the complexities remain the same also in the lightface case. In particular, we show that the family of all the closed Salem sets is $\Pi ^0_3$ -complete. We furthermore characterize the Weihrauch degree of the functions computing Hausdorff and Fourier dimension of closed sets.prepared by Manlio Valenti.E-mail:[email protected]. (shrink)

Inquieta anche il fatto che i nuovi giardini tendano ad assomigliare in modo impressionante a quei “rendering”, anch’essi uno standard, che si trovano esposti nelle vetrine delle sempre più numerose agenzie immobiliari che impestano la periferia diffusa. Ne avevo una vicino a casa qualche trasloco fa, quando abitavo in un appartamento di due stanze con bagno nel quartiere di Santa Lucia.Vitaliano Trevisan, Tristissimi giardini, pp. 46-47 Dopo la mela biblica consumata in un giardino terrestre...

Indonesia, like many other countries around the world, is currently experiencing the process of democratic backsliding, marked by a toxic mix of religious sectarianism, polarization, and executive overreach. Despite this trend, Indonesians have become more, rather than less, satisfied with their country's democratic practice. What accounts for this puzzle? Unity Through Division examines an overlooked aspect of democracy in Indonesia: political representation. In this country, an ideological cleavage between pluralism and Islamism has long characterized political competition. This cleavage, while divisive, (...) has been a strength of Indonesia's democracy, giving meaning to political participation and allowing a degree of representation not often observed in young democracies. While the recent resurgence of radical Islam and political polarization in Indonesian politics may have contributed to democratic erosion, these factors have simultaneously clarified political alternatives and improved perceptions of representation, in turn bolstering democratic participation and satisfaction. This compelling book effectively challenges the wisdom of the role of Islam in Indonesian political life and provides a fresh analysis for debates on democratic backsliding in Indonesia and beyond. (shrink)

Inquieta anche il fatto che i nuovi giardini tendano ad assomigliare in modo impressionante a quei “rendering”, anch’essi uno standard, che si trovano esposti nelle vetrine delle sempre più numerose agenzie immobiliari che impestano la periferia diffusa. Ne avevo una vicino a casa qualche trasloco fa, quando abitavo in un appartamento di due stanze con bagno nel quartiere di Santa Lucia.Vitaliano Trevisan, Tristissimi giardini, pp. 46-47 Dopo la mela biblica consumata in un giardino terrestre...

The aim of this article is to identify the main factors of the current crisis of the nation-state and to demonstrate how many of the voids left by this crisis are filled by religions. The main characteristic of the nation-state is the principle of sovereignty. The apogee of the nation-state is the political form of industrialization. National identity is possible only when the state proves to its citizens that the fact of being a member of it carries benefits and privileges (...) and will always bring more. Today, the majority of nation-states, in particular the oldest great powers, no longer have this capability. The weakening of the nation-state began at the end of the 19th century. The first wave of globalization multiplied the cases of reciprocal interferences and trespassed on the theoretical impermeability of the sovereign states. The outcome of the First World War, with the creation of the first supranational body, and much more the outcome of the Second World War, were two important steps of this crisis. The birth of the United Nations, and of other supranational bodies, as well as the creation of the first court called to judge an entire political class, were an assault on the principle of sovereignty. The second wave of globalization, characterized by the free circulation of goods, money, people and cultures, did the rest. Moreover, the countries that ‘invented’ the principle of sovereignty are today in relative decline as new powers are emerging. The nation-state is no longer able to keep its promises. The less effective states become at offering their citizens both meaning and social services, the more do religions tend to reoccupy the public stage. The less national and political legitimacy they have, the more powers use the religious tool against one another. (shrink)

Una prima parte del saggio sintetizza le linee principali di un recente libro dell’autore: Per un paradigma del corpo: una rifondazione filosofica dell’ecologia, Quodlibet, Macerata, 2019. Viene sostenuto un paradigma in cui corpo e biologia mantengano la loro irriducibilità nei confronti della cultura e in cui il cosiddetto “linguistic turn”, che ha dominato la filosofia del XX secolo, viene fortemente criticato; in coerenza con questo, la riflessione di Merleau-Ponty sul concetto di natura viene considerata lo strumento più adeguato e più (...) attuale per ripensare la questione ecologica; ne vengono esaminate le conseguenze nel campo della filosofia della tecnologia e del problema del soggetto. Una seconda parte del saggio, che si concentra sull’incontro che ebbe luogo nel 1961 fra Adorno e Merleau-Ponty, cerca di abbozzare un paradigma materialistico per l’ecologia, correggendo l’avvicinamento che alla fine della sua vita vi fu fra Merleau-Ponty e Heidegger. (shrink)

The emergence of ecology as a fundamental horizon not only of politics, but also of contemporary philosophy, pushes us to rethink the relationship that currents of thought such as Kuturkritik and phenomenology, especially the phenomenology of Maurice Merleau-Ponty, can maintain with it. After a preliminary consideration of post-structuralist and postmodern positions from this perspective, the essay focuses on the French philosopher, and in particular on his courses on Nature and on his elaboration of the Husserlian concept of Stiftung. This results (...) in Merleau-Ponty’s original position on the Kultur – Civilization alternative: critique of unlimited productivism, respect for the environment, and, at the same time, defense of the variety of cultures and traditions from a homogenizing globalization are valuable tools that his philosophy offers to the debates of our time. (shrink)

A recent meta-analysis by Munafò, Durrant, Lewis, and Flint [Munafò, M. R., Durrant, C., Lewis, G., & Flint, J. . Gene × environment interactions at the serotonin transporter locus. Biological Psychiatry, 65, 211–219] questioned the meaning of studies searching for endophenotypes associated with the serotonin-transporter-linked promoter region polymorphism, including our study on visual perspective during autobiographical memory retrieval. However, the association of 3rd person perspective with vulnerability for depression does not rely only on genetics. External consistency is provided by the (...) influence of the 5-HTTLPR polymorphism on brain regions involved in emotion regulation and autobiographical memory retrieval . Internal consistency is provided by the increased prevalence of 3rd person perspective in both currently and previously depressed patients, as well as in depression-prone individuals. Further studies should examine therapeutic opportunities. (shrink)

We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to $\mathrm {ATR_0}$ from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify eight different multivalued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility. In particular one of our functions turns out to be strictly (...) stronger than any previously studied multivalued functions arising from statements around $\mathrm {ATR}_0$. (shrink)

A Latin-American/Spanish edition of the medieval classic. Boethius' treatises on meditation and beauty are still valid to this very day.

In a well-known tradition, basically marked by the influence of Augustinian thought, the notion of divine omnipotence fixes the conceptual space of theology in the XI century, especially in accordance with the primacy of logical subjects. Among others, Anselm of Canterbury gives to XII century the opportunity to settle this conceptual reference, disclosing and organizing many argumentative solutions of the late scholastic period.