In this paper we first consider hyperfinite Borel equivalence relations with a pair of Borel $\mathbb {Z}$ -orderings. We define a notion of compatibility between such pairs, and prove a dichotomy theorem which characterizes exactly when a pair of Borel $\mathbb {Z}$ -orderings are compatible with each other. We show that, if a pair of Borel $\mathbb {Z}$ -orderings are incompatible, then a canonical incompatible pair of Borel $\mathbb {Z}$ -orderings of $E_0$ can be Borel embedded into the given pair. (...) We then consider hyperfinite-over-finite equivalence relations, which are countable Borel equivalence relations admitting Borel $\mathbb {Z}^2$ -orderings. We show that if a hyperfinite-over-hyperfinite equivalence relation E admits a Borel $\mathbb {Z}^2$ -ordering which is self-compatible, then E is hyperfinite. (shrink)

In this paper we consider the classes of all continuous $\mathcal {L}$ -(pre-)structures for a continuous first-order signature $\mathcal {L}$. We characterize the moduli of continuity for which the classes of finite, countable, or all continuous $\mathcal {L}$ -(pre-)structures have the amalgamation property. We also characterize when Urysohn continuous $\mathcal {L}$ -(pre)-structures exist, establish that certain classes of finite continuous $\mathcal {L}$ -structures are countable Fraïssé classes, prove the coherent EPPA for these classes of finite continuous $\mathcal {L}$ -structures, and (...) show that actions by automorphisms on finite $\mathcal {L}$ -structures also form a Fraïssé class. As consequences, we have that the automorphism group of the Urysohn continuous $\mathcal {L}$ -structure is a universal Polish group and that Hall’s universal locally finite group is contained in the automorphism group of the Urysohn continuous $\mathcal {L}$ -structure as a dense subgroup. (shrink)

We are living in an algorithmic age where mathematics and computer science are coming together in powerful new ways to influence, shape and guide our behaviour and the governance of our societies. As these algorithmic governance structures proliferate, it is vital that we ensure their effectiveness and legitimacy. That is, we need to ensure that they are an effective means for achieving a legitimate policy goal that are also procedurally fair, open and unbiased. But how can we ensure that algorithmic (...) governance structures are both? This article shares the results of a collective intelligence workshop that addressed exactly this question. The workshop brought together a multidisciplinary group of scholars to consider barriers to legitimate and effective algorithmic governance and the research methods needed to address the nature and impact of specific barriers. An interactive management workshop technique was used to harness the collective intelligence of this multidisciplinary group. This method enabled participants to produce a framework and research agenda for those who are concerned about algorithmic governance. We outline this research agenda below, providing a detailed map of key research themes, questions and methods that our workshop felt ought to be pursued. This builds upon existing work on research agendas for critical algorithm studies in a unique way through the method of collective intelligence. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:This volume collects seven articles of Carlo Paolazzi, O.F.M., previously published in journals and congress proceedings between 1996 and 2004, each of them dealing with the Writings of Francis. The essays are not arranged chronologically but move from more general to more specific studies on the Writings of Francis of Assisi. The titles of the essays included are: 1) The Birth of the Writings and Constitution of the Canon (...) ; 2) Francis, Theology and the Letter to brother Anthony ; 3) Anthony cites Francis: the Epilogue of the Sunday Sermons and the Early Rule XVI ; 4) The Writings between Francis and his secretaries: a Knot to be Untied ; 5) Concerning the Autographs of brother Francis: Doubts, Verifications and Confirmations ; 6) Concerning the Authenticity of the Writings of Francis to the "Poor Ladies" ; 7) The Lesser Brothers and Books: Concerning the Exegesis of "the books necessary to fulfill their office" and "Those who do not know how to read" . Each of the essays displays a careful methodology and appreciation for the evangelical content of the texts.The first essay deals with the establishment of the "canon" of Francis's writings in which the author demonstrates that the writings are born and develop from Francis's relationship with the Word of God. In this context, "writing" takes on the character of an "essential moment" in Francis's relationship with the Word , with God and with the brotherhood. This explains for Paolazzi, the passion with which Francis recommends the writings to those to whom they are addressed.The second and third essays are related to Anthony of Padua and the writings. The second essay deals with the content and authenticity of the Letter to Anthony, included by Kajetan Esser in the canon of Francis's writings. Paolazzi argues that the expression, "Brother Anthony my bishop" goes back to Francis himself. He suggests that Anthony's request for permission to teach reflects the concern of the novice who had permission from his minister to have a breviary, but was uncomfortable and needed Francis's explicit permission , a characteristic of the tension in the brotherhood upon Francis's return from Egypt in 1220. The conditions Francis places on the teaching of Anthony reflect Francis's concern that the Word of God not be approached purely from an intellectual perspective, but rather as a Word which must transform life. The third essay attempts to demonstrate that the Epilogue to Anthony's Sunday Sermons integrates sections of chapter 17 of the Early Rule. Paolazzi concludes this careful lexical study with the affirmation that Anthony had the Early Rule's exhortation to preachers in chapter 17 before his eyes as he concluded his Opus Evangeliorum .In the fourth essay Paolazzi tackles the question of the role played by secretaries in the production of the Writings of Francis. Scholars, including Esser, have suggested that because of his health and/or because of his status as "illiterate," Francis depended on secretaries to put his thoughts on paper. Paolazzi approaches the question by citing a saying attributed to Francis from the Mirror of Perfection . That this saying goes back to the historical Francis Paolazzi concludes based on both the content and the fact that it reflects Francis's literal approach to the Gospel. The saying states that Francis wanted no one to call him good, father or master because of the teaching of Christ in the Gospel who said that only God should be addressed with these titles . He then studies the usage and appearance of these three terms in the Writings of Francis, which confirm a consistent usage in accord with this saying. This demonstrates that the Writings reflect the "speech" of Francis and not simply his conceptual thought. Paolazzi considers that "in the Writings religious thought and the verbal lexicon of evangelical inspiration respond one to.. (shrink)

Che 1-p'yŏn. Ch'ŏndo wa inbŏp (inbŏpch'ŏn) -- 1. Kodae Chungguk ŭi inbŏpch'ŏn ch'ŏrhak sasang -- 2. Sŏnjin sidae ch'ŏnmyŏnggwan ŭi chŏn'gae -- 3. Sŏnjin sidae chŏnt'ong chaeigwan -- 4. Kunju wa minbon : Sŏnjin sidae kunju, minbollon kwa chŏhang, hyŏngmyŏng sasang -- 5. Ch'ŏndo ŭi naeyong kwa inbŏp ŭi panyŏng - Che 2-p'yŏn. Hangsang kwa pyŏnhwa -- 1. To ŭi hangsangsŏng kwa pyŏnhwasŏng -- 2. Pŏp ŭi hangsangsŏng kwa pyŏnhwasŏng -- 3. Pŏpchesasang hangsang kwa pyŏnhwa -- 4. Ch'im Ka-bon kwa (...) Yang Kye-ch'o ŭi pyŏnbŏmnon pigyo -- Che 3-p'yŏn. P'yŏnghwa ŭi pŏp kwa yebang pŏphak : punjaeng ŭi p'yŏnghwa haegyŏl kwa yebang. (shrink)