The situation of childhood and the adolescence in the Republic of Argentina as object of social politics is discussed from a clinical point of view. This matter seems to be connected to the problems of (personal) security, sometimes mingling the barrier that separates this from the way Justice fu..

We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is ε X ", and (2) "If X is a well-ordering, then so is φ(α, X)", where α is a fixed computable ordinal and φ represents the two-placed Veblen function. For the former statement, we show that ω iterations of the Turing jump are necessary in the proof and that the statement is equivalent to ${\mathrm{A}\mathrm{C}\mathrm{A}}_{0}^{+}$ over RCA₀. To prove the (...) latter statement we need to use ω α iterations of the Turing jump, and we show that the statement is equivalent to ${\mathrm{\Pi }}_{{\mathrm{\omega }}^{\mathrm{\alpha }}}^{0}{-\mathrm{C}\mathrm{A}}_{0}$ . Our proofs are purely computability-theoretic. We also give a new proof of a result of Friedman: the statement "if x is a well-ordering, then so is φ(x, 0)" is equivalent to ATR₀ over RCA₀. (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)

We prove that the maximal order type of the wqo of linear orders of finite Hausdorff rank under embeddability is φ2, the first fixed point of the ε-function. We then show that Fraïssé’s conjecture restricted to linear orders of finite Hausdorff rank is provable in +“φ2 is well-ordered” and, over , implies +“φ2 is well-ordered”.

We show that the maximal linear extension theorem for well partial orders is equivalent over RCA0 to ATR0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR0 over RCA0.

Este trabalho é uma continuação da pesquisa anterior apresentada no MES 11 (Marcone & Bortolucci, 2021), onde buscávamos entender o papel do ledor (leitor), pessoa que lê o teste para o deficiente visual durante uma avaliação. O trabalho realizado desde então e até o segundo semestre de 2022, seguindo as conclusões tiradas em nosso trabalho anterior, foi focado no estudo, compreensão e sistematização do processo de adaptação de itens, aqueles relacionados à matemática como desenhos, tabelas, gráficos, enunciados e tudo relacionado (...) à elaboração de questões de matemática, e à atividade do ledor de teste de matemática. Para tanto, foram realizadas entrevistas com três profissionais diretamente vinculados a esse tipo de atividade, com ampla experiência na atividade de adaptação de testes matemáticos, além da análise de referenciais teóricos sobre o tema. Apresentaremos os principais pontos abordados em cada entrevista, como a necessidade de o processo de adaptação do teste ocorrer simultaneamente à construção do teste, para que as intervenções necessárias possam ocorrer antes da montagem do teste ser concluída, seguido de uma discussão, com conclusões mostrando o quão importante é descrever uma imagem adequadamente, com o mínimo de informações, para que o candidato possa realizar o teste no tempo que tiver. Esta pesquisa foi avaliada por um comitê de ética independente e autorizada a ser realizada. (shrink)

Several DNA-damage detection and repair mechanisms have evolved to repair double-strand breaks induced by mutagens. Later in evolutionary history, DNA single- and double-strand cuts made possible immune diversity by V(D)J recombination and recombination at meiosis. Such cuts are induced endogenously and are highly regulated and controlled. In meiosis, DNA cuts are essential for the initiation of homologous recombination, and for the formation of joint molecule and crossovers. Many proteins that function during somatic DNA-damage detection and repair are also active during (...) homologous recombination. However, their meiotic functions may be altered from their somatic roles through localization, posttranslational modifications and/or interactions with meiosis-specific proteins. Presumably, somatic repair functions and meiotic recombination diverged during evolution, resulting in adaptations specific to sexual reproduction. BioEssays 27:795–808, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

We show that the quasi-order of continuous embeddability between finitely branching dendrites (a natural class of fairly simple compacta) is $\Sigma_1^1$ -complete. We also show that embeddability between countable linear orders with infinitely many colors is $\Sigma_1^1$ -complete.

We study the provability in subsystems of second-order arithmetic of two theorems of Harrington and Shelah [6] about Borel quasi-orderings of the reals. These theorems turn out to be provable in ATR0, thus giving further evidence to the observation that ATR0 is the minimal subsystem of second-order arithmetic in which significant portion of descriptive set theory can be developed. As in [6] considering the lightface versions of the theorems will be instrumental in their proof and the main techniques employed will (...) be the reflection principles and Gandy forcing. (shrink)

Resumen La argumentación es una forma de discurso en la que un hablante defiende una postura en una discusión. El presente trabajo se enfoca en la complejidad argumentativa y los recursos evaluativos y evidenciales que caracterizan las disputas de niños de diverso nivel socioeconómico. Se analizaron 94 disputas entre niños de 4 años y otros niños (5 a 10 años) en situaciones de juego espontáneo registradas en hogares de sectores socioeconómicos medio y bajo. El análisis identificó diferencias marginales en la (...) complejidad argumentativa entre los grupos. Por su parte se hallaron diferencias significativas en recursos de evaluativos de emocionalidad y en los evidenciales deónticos y exclamativos a favor de los sectores de nivel socioeconómico bajo. Los sectores medios registraron un mayor empleo de expresiones de causalidad y conectores. Los resultados se discuten a la luz de los hallazgos de investigaciones previas. Abstract Argumentation is a type of discourse in which a speaker defends a claim in a discussion. The present work focuses on the argumentative complexity and the evaluative and evidential resources that characterize the disputes of children of different socioeconomic levels. We analyzed 94 disputes between 4-year-old children and other children (5 to 10 years old) in situations of spontaneous play registered in homes of middle and low socioeconomic status (SES). The analysis identified marginal differences in argumentative complexity between the groups. On the other hand, significant differences were found in evaluative expressions of emotion and in deontic and exclamatory evidential markers, more frequently used by the low SES group. The mid SES group tends to use a higher number of expressions of causality and connectors. The results are discussed with reference to the findings of previous research. (shrink)

D. Jacquart / A. Paravicini Bagliani (textes reunis par), Le Moyen.ge et les sciences, SISMEL-Edizioni del Galluzzo, Firenze 2021 (Micrologus Library, 100).

From Hippocrates and Galen, meteorological medicine studied the impact of environmental factors and weather phenomena on mental and bodily health. This theory has been largely diffused by medical works and encyclopaedias, such as those of Vincentius de Beauvais and Bartholomeus Anglicus. However, its reception within mediaeval meteorology still remains to be fully inquired, partly because it was not a traditional topic to be discussed in the question commentaries on the Meteorologica of Aristotle. This article aims to focus on three Parisian (...) quaestiones on the Meteorologica in which Radulphus Brito and Themo Iudaei de Monasterio utilised concepts of meteorological medicine as a tool to explain meteorological principles. The medical theory is used to clarify how antiperistasis works within animals’ bellies and its impacts on their general health; and in the second one, to describe the harmful impacts water has on human and animal bodies; and then thirdly, to explain the process of generating rain. (shrink)

The growth of consumer DNA ancestry testing has resulted in questions and critiques being raised in social and research contexts. This study examined individuals discussing their ancestry DNA testing results on YouTube by searching for the two most popular testing companies (23andMe; Ancestry) and the phrase “DNA results.” The finalized dataset consisted of 117 videos, on which directed content analysis was performed. In the videos, individuals used results to clarify, confirm, question, and re-evaluate their previously held conceptions of racial/ethnic identities. (...) Reactions were more positive than negative (88.1% vs. 8.1%), and results more commonly reaffirmed (77.8%) than re-conceptualized (40.0%) one’s racial/ethnic identity. Ancestry testing and personal social media accounts were commonly promoted, demonstrating biotechnological hype where promotion abounds and critiques are scarce. Questions persist around the impact of ancestry DNA testing in reifying a scientifically inaccurate conception of race and what impact YouTube videos might have on audiences. (shrink)

We study the reverse mathematics of interval orders. We establish the logical strength of the implications among various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain 2 \oplus 2. We also study proper interval orders and their characterization theorem: a partial order is a proper interval order if and only if it (...) contains neither 2 \oplus 2 nor 3 \oplus 1. (shrink)

The purpose of this succinct work is to present N. Machiavelli's classic republican view from his proposition of an inevitable paradox, the founding of an expansionist republic, difficult to govern, or the founding of a stable, but small and weak republic. Such a paradox, according to Machiavelli, should direct and condition all the constitutive devices of the republic when choosing what will be its destiny as a political body. The model of republic preferred by the Florentine will be the expansionist (...) model of Rome, leading him to assume all the devices that gave this republic its power. From this presentation of the Machiavellian proposition, we will analyse the assimilation of republican thought in England from the Elizabethan period, as well as the political-social scenario that exists there. This itinerary will allow us to understand, in general, why classical republicanism was received on English soil from the perspective of establishing a mixed, stable government, thus favouring the spread of the Venice myth as a serene republic and delaying the use, even that mitigated, of the republican presuppositions expressed in the Machiavellian work that directed towards a Roman model. (shrink)

Neste breve artigo, argumentaremos que a pandemia da Covid-19, como outras na história humana, colocou em desnudo as bases da estrutura político-econômica moderna. Defenderemos que tais bases apoiam-se em dois esteios, uma noção política de ‘Estado’, ápice da organização humana, e uma concepção racionalista, técnica e produtiva, que promulga a possibilidade de resposta a qualquer crise surgida na sociedade. Como contrapondo a esta estrutura, apresentaremos a teoria maquiaveliana, que aponta para uma relação indelével entre política e fator natural, natureza e (...) sociedade. Nesta teoria, com uma concepção antropológica própria, as necessidades impostas pela natureza frente a ação humana são determinantes para se pensar a própria construção política. Como resultado, consideraremos ser necessário repensar a estrutura político-econômica moderna em seus pretensos mitos de incontestável avanço político, por meio do ‘Estado’, e inabalável base racional, principalmente técnico-produtiva, retomando o lugar de importância do fator natural para constituição de uma sociedade mais ‘humana’. (shrink)

Tencionamos, neste artigo, demonstrar os meandros constitutivos do que seja um formalismo moral em Immanuel Kant, tendo como pressuposto teórico sua compreensão de uma teoria da vontade. Este movimento de análise e demonstração teórica terá como fio condutor a ideia de autonomia que permeia a construção da vontade no formalismo kantiano, ou seja, a pressuposição de uma possível autonomia formal da razão é a base na qual se assenta a teoria moral deste pensador. Para execução de nossa pretensão será necessário (...) reconstituir os pontos nevrálgicos do que venha a ser uma teoria da vontade para em seguida analisar os pressupostos kantianos que realçam a centralidade da autonomia da razão na compreensão de uma vontade livre. Desta maneira, o que se pretende por em desnudo é a originalidade kantiana, em relação à tradição que promulga a vontade como marca da liberdade humana, a partir de seu pressuposto de autonomia formal na constituição moral do indivíduo humano. (shrink)

Neste artigo intentamos empreender uma leitura do judaísmo antigo, ou veterotestamentário, em alguns de seus aspectos principais, à contraluz da visão maquiaveliana do papel da religião na organização e expansão do Estado. O primeiro passo desta empresa será dado ao expormos os traços fundantes e delineadores da tradição judaica antiga, principalmente nos livros que compõe o chamado velho testamento, demonstrando o uso da religião na ordenação e expansão do Estado, bem como na formação do indivíduo. Em um segundo momento demonstraremos (...) como se cria uma nova tradição judaica, influenciada e influenciadora do mundo grego antigo, logo no início da era cristã a qual será assimilada e explorada em seu viés místico no humanismo renascentista. Esta tradição judaico helenístico será a mais conhecida e assimilada nos círculos eruditos europeus da renascença. Por fim, buscaremos demonstrar como os traços constitutivos do judaísmo antigo, em detrimento ao judaísmo helenístico, podem ser lidos à luz da descrição maquiaveliana do papel da religião na organização e expansão do Estado e na formação do indivíduo. (shrink)

Our objective in this brief article is guided by the demonstration of the existence of a theory of political action in Machiavelli's republican thought, with such a theory having its own character that directs it to highlight the action of individuals in the social context. In addition to this objective, we hope to support the thesis that such a theory of political action has a republican scope, not just “republicanist”, in keeping with the Machiavellian preference for institutions that impress on (...) individuals a civic sense based above all on the materiality of political action in the body social. From this assertion, we indicate that our itinerary will be guided by the demonstration of the search for the valorization of political action in Machiavelli's theory, the materiality of such action, to the detriment of its pure intention, the central focus of Florentine's work. This disposition of the centrality of political action in Machiavelli republicanism will underscore its appreciation for outlining the political functions of the search for recognition, glory and especially the benefit of the political body as a whole. (shrink)

In this brief article we will seek to support the thesis that there is in the thought of Coluccio Salutati, 14th century Florentine chancellor and prominent humanist, a clear republicanism that turns to the issue of the freedom of the republic and the active life of the individuals participating in it. However, in connection with this demonstration, we will also maintain that such republicanism has strong traces of Augustinian influence, mainly in view of the disposition of laws in the political (...) arrangement, as well as the relationship between active life and the search for a human being’s own good. In view of this, we intend to demonstrate that, in general, Salutati’s Renaissance republicanism turns to the defence of the republic, its freedom and its characteristic of the proper scenario for the active life of individuals, however, it still maintains an ethical-political perspective typical of the medieval period, centrally influenced by Augustinian thought. (shrink)

Tencionamos, neste artigo, tratar da questão da imitação no pensamento maquiaveliano. Tomaremos como balizas suas postulações acerca da natureza do homem, as possibilidades de formatação de uma república profícua em vista desta natureza e o papel dos exemplos dos indivíduos que agem em prol do bem da república. Sendo a questão da imitação o fio condutor, elegeremos ainda um tripé para demonstrar nossa hipótese, a saber, o fator antropológico; o fator educacional; o fator político. Por este movimento, pretende-se demonstrar que (...) a aparente negatividade das postulações maquiavelianas sobre a natureza humana não inviabilizam a promulgação de uma república estável, tendo os bons exemplos políticos um papel preponderante neste propósito. (shrink)

The intention of this brief article is to demonstrate, through the Machiavellian and Shakespearean analyzes, mediated by the latter's work, “The Merchant of Venice”, the contrast between the classical republican conception and the modern political ideal of freedom. We will take as a gauge the ideas of social belonging (religion, social recognition); legal constitution of rights (individual freedom), trying to understand how these aspects are constructed in the representations of the city of Venice by the two authors. For this undertaking, (...) it will be necessary to understand the Machiavellian understanding of the political and social structures that founded and sustained the Venice of his time. Then understand the scenario in which Shakespeare sees the Venice of his era, analyzing his work mentioned. Finally, we will try to demonstrate how one can extract from this intricate approximation subsidies to think the contrast between the traces of a classic republican thought and the incipient points of a modern conception of individual freedom. (shrink)

In (Fund Math 60:175–186 1967), Wolk proved that every well partial order (wpo) has a maximal chain; that is a chain of maximal order type. (Note that all chains in a wpo are well-ordered.) We prove that such maximal chain cannot be found computably, not even hyperarithmetically: No hyperarithmetic set can compute maximal chains in all computable wpos. However, we prove that almost every set, in the sense of category, can compute maximal chains in all computable wpos. Wolk’s original result (...) actually shows that every wpo has a strongly maximal chain, which we define below. We show that a set computes strongly maximal chains in all computable wpo if and only if it computes all hyperarithmetic sets. (shrink)

Name der Zeitschrift: Millennium Jahrgang: 13 Heft: 1 Seiten: 41-46.

O presente artigo, de natureza bibliográfica, objetiva discutir alguns desafios políticos e epistemológicos postos aos movimentos sociais e à educação popular no contexto das sociedades complexas. Parte-se do reconhecimento que estamos vivendo, nas últimas décadas, transformações profundas que impactam em todas as dimensões da vida tanto individual quanto social. Esses processos ocorrem em espaços locais, mas impactam globalmente, assim como existem tendências globalizantes que impactam nos espaços locais, na subjetividade e nas relações intersubjetivas. O incremento de tecnologias acelera esses processos, (...) trazendo implicações políticas, pedagógicas, sociais e culturais. Um conjunto de mudanças em curso ainda são de difícil avaliação dado que são movimentos em curso, mas, nem por isso, deixam de colocar novas exigências epistêmicas e políticas, ou seja, as realidades emergentes sempre desafiam a construção de novos referenciais e novas práticas. Os movimentos sociais e a educação popular não estão imunes a essas influências. Daí o desafio para pensar o emergente atentando para o residual e o dominante, conforme propõe Raymond Williams, visto que estão profundamente imbricados. Nesse contexto, questiona-se a respeito das contribuições de referenciais clássicos, tanto das ciências sociais quanto pedagógicas, na análise da realidade e na fundamentação de projetos emancipatórios. Buscando dar conta dessas questões, o texto inicia contextualizando algumas tendências no âmbito do eixo temático “educação popular e movimentos sociais” tendo como base as dez edições da Anpedsul e segue com um diagnóstico das transformações em curso que tornam as sociedades complexas. Na sequência, são analisados alguns desafios políticos e epistemológicos visando a dar conta de uma compreensão mais ampla dos complexos fenômenos emergentes e, para concluir, uma reflexão sobre o papel dos clássicos nas investigações e pesquisas relativas aos movimentos sociais e a educação popular. Palavras-chave: Movimentos sociais. Educação popular. Política. Epistemologia. Sociedades complexas. (shrink)

This article explores a key question in the history of science: Could untrained officials learn and apply practical knowledge by reading how-to books and collaborating with expert practitioners? Notably, historians of science have studied workplaces such as the mines as arenas of knowledge exchange between workers, expert practitioners, and learned humanists. This article uses a labor history approach to explore what this exchange meant in practice. It analyzes the attempts of an untrained official in the mines of the Medici family (...) to learn and reproduce practical knowledge about prospecting and surveying. By the mid-sixteenth century, this official read Georg Agricola’s (1494–1555) mining treatises and had access to the expertise of German miners from the renowned mining districts of Central Europe. The analysis of his reports based on the reading of the book, along with the hierarchical organization of labor established by the German experts in the Medici mines, reveals that the presence of craftsmen and scholarly works reinforced, rather than blurred, the boundaries of knowledge in early modern mines. (shrink)

In this paper we give a proof of the II12-completeness of the set of countable better quasi orderings . This result was conjectured by Clote in [2] and proved by the author in his Ph.d. thesis [6] . Here we prove it using Simpson's definition of better quasi ordering and as little bqo theory as possible.

Let ${\cal I}$ be an ideal on ω. By cov${}_{}^{\rm{*}}$ we denote the least size of a family ${\cal B} \subseteq {\cal I}$ such that for every infinite $X \in {\cal I}$ there is $B \in {\cal B}$ for which $B\mathop \cap \nolimits X$ is infinite. We say that an AD family ${\cal A} \subseteq {\cal I}$ is a MAD family restricted to${\cal I}$ if for every infinite $X \in {\cal I}$ there is $A \in {\cal A}$ such that $|X\mathop (...) \cap \nolimits A| = \omega$. Let a$\left$ be the least size of an infinite MAD family restricted to ${\cal I}$. We prove that If $max${a,cov${}_{}^{\rm{*}}\}$ then a$\left = {\omega _1}$, and consequently, if ${\cal I}$ is tall and $\le {\omega _2}$ then a$\left = max$ {a,cov${}_{}^{\rm{*}}\}$. We use these results to prove that if c$\le {\omega _2}$ then o$= \overline o$ and that as$= max${a,non$\}$. We also analyze the problem whether it is consistent with the negation of CH that every AD family of size ω1 can be extended to a MAD family of size ω1. (shrink)

This work examines whether the environmentally-induced decoherence approach in quantum mechanics brings us any closer to solving the measurement problem, and whether it contributes to the elimination of subjectivism in quantum theory. A distinction is made between ,collapse, and ,decoherence,, so that an explanation for decoherence does not imply an explanation for collapse. After an overview of the measurement problem and of the open-systems paradigm, we argue that taking a partial trace is equivalent to applying the projection postulate. A criticism (...) of Zurek's decoherence approach to measurements is also made, based on the restriction that he must impose on the interaction between apparatus and environment. We then analyze the element of subjectivity involved in establishing the boundary between system and environment, and criticize the incorporation of Everett's branching of memory records into the decoherence research program. Sticking to this program, we end by sketching a proposal for ‘environmentally-induced collapse’. (shrink)

Osvaldo Guariglia presenta tres modelos paradigm ticos: la propuesta kantiana de una fundamentaci n absoluta basada en la estructura prescriptiva de la raz n pr ctica; la propuesta hegeliana, que intenta superar cr ticamente la de Kant y, por ltimo, la propuesta weberiana, punto de partida de la moderna sociolog a pol tica.

En Política VI 2, 1317b 1-17, Aristóteles define así la democracia: «el rasgo esencial de la democracia es el vivir como se quiere sin ninguna interferencia y de aquí vino el de no ser gobernado, si es posible por nadie, y si no, por turnos. Esta característica contribuye a un sistema general de la libertad fundada en la igualdad». Este modelo normativo dio lugar, históricamente, a dos posibles regímenes políticos, la democracia popular o extrema, basada en la participación directa de (...) todos los ciudadanos, como en Atenas, y una «constitución mixta» que tenía rasgos tanto democráticos como oligárquicos, llamada república en la tradición romana desde Cicerón. La democracia moderna es la heredera de ambos regímenes, moderada por la nueva concepción de los derechos individuales que son propios del pensamiento moderno desde Hugo Grotius hasta la Declaración Universal de los Derechos Humanos. La constitución representativa fue, así, la solución moderna al conflicto entre gobierno de la mayoría y gobierno de las leyes. Desde su Independencia en el siglo XIX, las democracias de América Latina sufren por la tensión no resuelta entre populismo y constitución liberal democrática. El neo-populismo que surgió en los últimos años del siglo XX se presentó como un desafío y una respuesta a las promesas incumplidas de la democracia. Contra los defensores del populismo autoritario, como por ejemplo Ch. Mouffe y E. Laclau, yo sostengo que la democracia deliberativa es una respuesta superior a esas promesas. (shrink)

Comúnmente percibido como un elemento neutral e inocente, incluso un componente aliado e indispensable en las aspiraciones de proyectos sociales alternativos, la primera parte de este artículo se dedica a problematizar el valor de uso, subrayando el particular fetichismo que le es inherente. Su tratamiento crítico se complementa con un detenido estudio de la forma natural, dimensión imprescindible sin la que la crítica de la economía política quedaría inconclusa. El artículo pretende, entonces, en primer lugar, poner al descubierto la problemática (...) del valor de uso a lo interno de la obra de Karl Marx. Seguidamente, se observará su particular fetichismo rescatando argumentos feministas, antropológicos y filosóficos que ayuden a apreciar su dimensión y carácter históricamente específico. A continuación, se profundizará la forma natural y sus principales características, registro sin el cual la dimensión problemática del valor de uso no se comprendería. Acudiendo a los planteamientos de Bolívar Echeverría, se revisitará la forma natural puntualizando la dimensión semiótica como un componente central suyo. Finalmente, el texto cierra poniendo al descubierto las facetas, trampas y problemáticas inherentes a estas dos nociones, reivindicando la importancia de distinguirlas en un momento de desafíos ecológicos donde repensar el intercambio metabólico con el medio ambiente se torna crucial para la humanidad. (shrink)

If $\mathcal{F}$ is a filter on $\omega$, we say that $\mathcal{F}$ is Canjar if the corresponding Mathias forcing does not add a dominating real. We prove that any Borel Canjar filter is $F_{\sigma}$, solving a problem of Hrušák and Minami. We give several examples of Canjar and non-Canjar filters; in particular, we construct a $\mathsf{MAD}$ family such that the corresponding Mathias forcing adds a dominating real. This answers a question of Brendle. Then we prove that in all the “classical” models (...) of $\mathsf{ZFC}$ there are $\mathsf{MAD}$ families whose Mathias forcing does not add a dominating real. We also study ideals generated by branches, and we uncover a close relation between Canjar ideals and the selection principle $S_{\mathrm{fin}}$ on subsets of the Cantor space. (shrink)

In quest’articolo, articolo prenderò in esame i passi in cui Kant descrive la monadologia leibniziana come un “concetto platonico” del mondo, ossia come una descrizione del mondo intelligibile che non ha nulla a che vedere con la spiegazione del mondo fenomenico. In generale, vorrei mostrare che quest’interpretazione non va contrapposta a quella che lo stesso Kant aveva dato nella prima Critica, dove la monadologia era caratterizzata come un “sistema intellettuale del mondo”. Per fare ciò, risponderò a due domande. La prima (...) riguarda le ragioni che possono aver indotto Kant, in diverse occasioni, a presentare Leibniz come un precursore della teoria della soggettività dello spazio. La seconda riguarda il motivo per cui Kant associa costantemente la monadologia alla teoria platonica delle idee, mostrando come, in entrambi i casi, Kant intenda criticare qualsiasi possibilità di un transito dal mondo sensibile a quello intelligibile. Infine, cercherò di mostrare che, dietro questa lettura deflazionista della monadologia, c’è anche un’implicita autocritica alle tesi che Kant stesso ha sostenuto nella Dissertatio del 1770. (shrink)

The main topics of this thesis are cardinal invariants, P -points and MAD families. Cardinal invariants of the continuum are cardinal numbers that are bigger than $\aleph _{0}$ and smaller or equal than $\mathfrak {c}.$ Of course, they are only interesting when they have some combinatorial or topological definition. An almost disjoint family is a family of infinite subsets of $\omega $ such that the intersection of any two of its elements is finite. A MAD family is a maximal almost (...) disjoint family. An ultrafilter $\mathcal {U}$ on $\omega $ is called a P-point if every countable $\mathcal {B\subseteq U}$ there is $X\in $ $\mathcal {U}$ such that $X\setminus B$ is finite for every $B\in \mathcal {B}.$ This kind of ultrafilters has been extensively studied, however there is still a large number of open questions about them.In the preliminaries we recall the principal properties of filters, ultrafilters, ideals, MAD families and cardinal invariants of the continuum. We present the construction of Shelah, Mildenberger, Raghavan, and Steprāns of a completely separable MAD family under $\mathfrak {s\leq a}.$ None of the results in this chapter are due to the author.The second chapter is dedicated to a principle of Sierpiński. The principle $\left $ of Sierpiński is the following statement: There is a family of functions $\left \{ \varphi _{n}:\omega _{1}\longrightarrow \omega _{1}\mid n\in \omega \right \} $ such that for every $I\in \left [ \omega _{1}\right ] ^{\omega _{1}}$ there is $n\in \omega $ for which $\varphi _{n}\left [ I\right ] =\omega _{1}.$ This principle was recently studied by Arnie Miller. He showed that this principle is equivalent to the following statement: There is a set $X=\left \{ f_{\alpha }\mid \alpha \alpha $ then $f_{\beta }\cap g$ is infinite. Miller showed that the principle of Sierpiński implies that non $\left =\omega _{1}.$ He asked if the converse was true, i.e., does non $\left =\omega _{1}$ imply the principle $\left $ of Sierpiński? We answer his question affirmatively. In other words, we show that non $\left =\omega _{1}$ is enough to construct an $\mathcal {IE}$ -Luzin set. It is not hard to see that the $\mathcal {IE}$ -Luzin set we constructed is meager. This is no coincidence, because with the aid of an inaccessible cardinal, we construct a model where non $\left =\omega _{1}$ and every $\mathcal {IE}$ -Luzin set is meager.The third chapter is dedicated to a conjecture of Hrušák. Michael Hrušák conjectured the following: Every Borel cardinal invariant is either at most non $\left $ or at least cov $\left $. Although the veracity of this conjecture is still an open problem, we were able to obtain some partial results: The conjecture is false for “Borel invariants of $\omega _{1}^{\omega }$ ” nevertheless, it is true for a large class of definable invariants. This is part of a joint work with Michael Hrušák and Jindřich Zapletal.In the fourth chapter we present a survey on destructibility of ideals and MAD families. We prove several classic theorems, but we also prove some new results. For example, we show that every almost disjoint family of size less than $\mathfrak {c}$ can be extended to a Cohen indestructible MAD family is equivalent to $\mathfrak {b=c}$. A MAD family $\mathcal {A}$ is Shelah–Steprāns if for every $X\subseteq \left [ \omega \right ] ^{<\omega }\setminus \left \{ \emptyset \right \} $ either there is $A\in \mathcal {I}\left $ such that $s\cap A\neq \emptyset $ for every $s\in X$ or there is $B\in \mathcal {I}\left $ that contains infinitely many elements of X $ denotes the ideal generated by $\mathcal {A}$ ). This concept was introduced by Raghavan which is connected to the notion of “strongly separable” introduced by Shelah and Steprāns. We prove that Shelah–Steprāns MAD families have very strong indestructibility properties: Shelah–Steprāns MAD families are indestructible for “many” definable forcings that does not add dominating reals. According to the author’s best knowledge, this is the strongest notion that has been considered in the literature so far. In spite of their strong indestructibility, Shelah–Steprāns MAD families can be destroyed by a ccc forcing that does not add unsplit or dominating reals. We also consider some strong combinatorial properties of MAD families and show the relationships between them.The fifth chapter is one of the most important chapters in the thesis. A MAD family $\mathcal {A}$ is called $+$ -Ramsey if every tree that branches into $\mathcal {I}\left $ -positive sets has an $\mathcal {I}\left $ -positive branch. Michael Hrušák’s first published question is the following: Is there a $+$ -Ramsey MAD family? It was previously known that such families can consistently exist. However, there was no construction of such families using only the axioms of ZFC. We solve this problem by constructing such a family without any extra assumptions.In the fourth and fifth chapters, we introduce several notions of MAD families, in the sixth chapter we prove several implications and non implications between them. We construct several MAD families with different properties.In the seventh chapter we build models without P -points. We show that there are no P -points after adding Silver reals either iteratively or by the side by side product. These results have some important consequences: The first one is that is its possible to get rid of P -points using only definable forcings. This answers a question of Michael Hrušák. We can also use our results to build models with no P -points and with arbitrarily large continuum, which was also an open question. These results were obtained with David Chodounský.prepared by Osvaldo Guzmán GonzálezE-mail : oguzman@matmor.unam.mxURL : https://arxiv.org/abs/1810.09680. (shrink)

There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König's Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multivalued function Sep and a natural notion of reducibility for multivalued functions, we obtain a computational counterpart of the subsystem of second-order arithmetic WKL0. We study analogies and differences between WKL0 and the class (...) of Sep-computable multivalued functions. Extending work of Brattka, we show that a natural multivalued function associated with the Hahn-Banach Extension Theorem is Sep-complete. (shrink)

We continue with the study of the Katětov order on MAD families. We prove that Katětov maximal MAD families exist under $\mathfrak {b=c}$ and that there are no Katětov-top MAD families assuming $\mathfrak {s\leq b}.$ This improves previously known results from the literature. We also answer a problem form Arciga, Hrušák, and Martínez regarding Katětov maximal MAD families.

Este artículo investiga dos problemas principales en los conocidos argumentos de San Agustín en pro de la certeza, contra los escépticos. En realidad, son más bien dos niveles de una misma cuestión "metodológica": la interioridad del conocimiento y la reflexión, como vía de certeza. Conclusión principal de este estudio es que ambas dimensiones son correlativas: la reflexión supone interioridad, N la interioridad exige reflexión, como ría de certeza. La última parte del artículo examina la doctrina agustiniana de la reflexión, (...) en el contexto de su "filosofía del espíritu". La presente investigación intenta mostrar en este punto que, de hecho, San Agustín tematiza o supone, a lo largo de su obra tres grandes modos de reflexión, correspondientes a otros tantos modos de autoconocimiento del alma: el noticial, el cogitativo y el fenomenológico. (shrink)

Distensión de la finitud y belleza son paralelas en Agustín, su deducción y su calificación estética. Ontología de lo finito es, por ello, a la vez, discurso estético en tres grandes dimensiones: a) fundación y estructura de lo finito; b) sucesión temporal ; c) devenir histórico . Podríamos, sin reduccionismo alguno, interpretar su doctrina estética como >?.Distension of the finiteness and beauty are parallel in St. Augustine, its deduction and its aesthetic qualification. Ontology of finiteness is therefore, at the (...) same time, aesthetic thought in three dimensions: a) foundation and structure of the finetenesss; b) temporal succession ; c) historic becoming . Could we, with no reduction, interpret his aesthetic doctrine as >? (shrink)