We continue the investigation of the Laver ideal ℓ 0 and Miller ideal m 0 started in [GJSp] and [GRShSp]; these are the ideals on the Baire space associated with Laver forcing and Miller forcing. We solve several open problems from these papers. The main result is the construction of models for $t , where add denotes the additivity coefficient of an ideal. For this we construct amoeba forcings for these forcings which do not add Cohen reals. We show that (...) c = ω 2 implies $\operatorname{add}(m^0) \leq \mathfrak{h}$ . We show that b = c, d = c implies $\operatorname{cov}(\ell^0) \leq \mathfrak{h}^+, \operatorname{cov}(m^0) \leq \mathfrak{h}^+$ respectively. Here $\operatorname{cov}$ denotes the covering coefficient. We also show that in the Cohen model $\operatorname{cov}(m^0) holds. Finally we prove that Cohen forcing does not add a superperfect tree of Cohen reals. (shrink)

We continue [21] and study partition numbers of partial orderings which are related to /fin. In particular, we investigate Pf, be the suborder of /fin)ω containing only filtered elements, the Mathias partial order M, and , ω the lattice of partitions of ω, respectively. We show that Solomon's inequality holds for M and that it consistently fails for Pf. We show that the partition number of is C. We also show that consistently the distributivity number of ω is smaller than (...) the distributivity number of /fin. We also investigate partitions of a Polish space into closed sets. We show that such a partition either is countable or has size at least D, where D is the dominating number. We also show that the existence of a dominating family of size 1 does not imply that a Polish space can be partitioned into 1 many closed sets. (shrink)

In this paper we investigate the structure of uncountable maximal antichains of Silver forcing and show that they have to be at least of size d, where d is the dominating number. Part of this work can be used to show that the additivity of the Silver forcing ideal has size at least the unbounding number b. It follows that every reasonable amoeba Silver forcing adds a dominating real.

Drawing on newspaper articles, ad campaigns, declassified government archives, and old movies, Ken Hollings shows the culture of postwar America and its dream of limitless technological and human development.

In the early years of the twentieth century, the so-called ‘postulate analysis’—the study of systems of axioms for mathematical objects for their own sake—was regarded by some as a vital part of the efforts to understand those objects. I consider the place of postulate analysis within early twentieth-century mathematics by focusing on the example of a group: I outline the axiomatic studies to which groups were subjected at this time and consider the changing attitudes towards such investigations.

A family A ⊆ ℘(ω) is called countably splitting if for every countable $F \subseteq [\omega]^{\omega}$ , some element of A splits every member of F. We define a notion of a splitting tree, by means of which we prove that every analytic countably splitting family contains a closed countably splitting family. An application of this notion solves a problem of Blass. On the other hand we show that there exists an $F_{\sigma}$ splitting family that does not contain a closed (...) splitting family. (shrink)

First paragraph: The 'Beyond' of the theologians," to which Josef Mitterer alluded in a footnote in his 1988 essay "Farewell to the truth," can be understood as an offer of ultimate self-perception -- albeit with a high conflict potential.

Let ${{\mathcal J}\,(\mathbb M^2)}$ denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of ${{\mathcal J}\,(\mathbb M^2)}$ is bigger than the covering number of the ideal of the meager subsets of ω ω. We also show that Martin’s Axiom implies that the additivity of ${{\mathcal J}\,(\mathbb M^2)}$ is 2 ω .Finally we prove that there are no analytic infinite maximal antichains in any finite product of ${\mathfrak{P}{(\omega)}/{\rm fin}}$.

We show that every analytic set in the Baire space which is dominating contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. We call this property of analytic sets u-regularity. However, we show that the concept of uniform tree does not suffice to characterize dominating analytic sets in general. We construct a dominating closed set with the property that for no uniform tree whose (...) branches are contained in the closed set, the set of these branches is dominating. We also show that from a Σ1n+1-rapid filter a non-u-regular Π1n-set can be constructed. Finally, we prove that ∑12-Kσ-regularity implies ∑12-u-regularity. (shrink)

We prove that consistently the Lebesgue null ideal is not Tukey reducible to the Silver null ideal. This contrasts with the situation for the meager ideal which, by a recent result of the author, Spinas [Silver trees and Cohen reals, Israel J. Math. 211 473–480] is Tukey reducible to the Silver ideal.

Mirror-touch synaesthesia is a condition where observing touch to another’s body induces a subjective tactile sensation on the synaesthetes body. The present study explores which characteristics of the inducing stimulus modulate the synaesthetic touch experience. Fourteen mirror-touch synaesthetes watched videos depicting a touch event while indicating whether the video induced a tactile sensation, on which side of their body they felt this sensation and the intensity of the experienced sensation. Results indicate that the synaesthetes experience stronger tactile sensations when observing (...) touch to real bodies, whereas observing touch to dummy bodies, pictures of bodies and disconnected dummy body parts elicited weaker sensations. These results suggest that mirror-touch synaesthesia is not entirely bottom-up driven, but top-down information, such as knowledge about real and dummy body parts, also modulate the intensity of the experience. (shrink)

*Weitere Angaben Inhalt: Mit der Frage nach der Zuständigkeit der eigenen Nase in Religionsangelegenheiten beginnt diese ungewöhnliche Reise in Erfahrungsbereiche, die von Theologen bislang eher gemieden wurden. Nicht der Inhalt von Glaubensbekenntnissen ist Gegenstand des Interesses, sondern der Tonfall, in dem sie vorgetragen werden. Von bestimmten Kirchengerüchen geht die Rede, von Körperhaltungen beim Gottesdienst, von Kindheitserinnerungen und vom Läuten der Glocken. Dabei stellt sich heraus, dass mit dem abgenützten Etikett des Religiösen die Sinnenfälligkeit des Erlebten nur sehr oberflächlich bezeichnet wird.

We show that in the Silver model the inequality $\mathrm {cov}(\mathfrak {C} _2) < \mathrm {cov}(\mathfrak {P}_2)$ holds true, where $\mathfrak {C}_2$ and $\mathfrak {P}_2$ are the two-dimensional Mycielski ideals.

We describe a list of canonical functions from 2 to ℝ such that every Borel measurable function from 2 to ℝ, on some superperfect rectangle, induces the same equivalence relation as some canonical function.

Eine marktparadigmatische Wettbewerbsorientierung – symptomatisch die Exzellenzinitiative – hat die deutsche Hochschullandschaft radikal verändert und das Legitimationserfordernis gegenüber der Bürgerschaft verschärft. Hier setzt das Buch an und liefert eine dezidiert normative Fundierung für die legitime Gestaltung von Politik in der Demokratie im Hinblick auf die praktische Fruchtbarmachung für die deutsche Hochschulpolitik. Die Autorin bedient sich der legitimatorischen Ansätze von John Rawls im Sinne einer allgemeinen rationalen Zustimmungsfähigkeit und von John Dewey im Rahmen einer praktizierten sozialen Kooperation. Dewey wird weniger als (...) Gegenspieler zu Rawls, sondern als eine – pragmatistische – Komplettierung der Rawls‘schen Legitimationstheorie hinsichtlich der sozialen Praxis verstanden. Die abstrakten, politik-philosophischen Erörterungen werden dann im Hinblick auf ihre praktischen Implikationen für die Hochschulpolitik konkretisiert. Ein kooperatives, vertrauensvolles Zusammenwirken von gestärkter wissenschaftlicher und politischer Verantwortung sieht die Autorin als Weg hin zu einer lebendigen zivilgesellschaftlichen Öffentlichkeit und illustriert dies am Beispiel Wissenschaftsregionen. Die Arbeit verdeutlicht eine der bedeutenden Stärken der politischen Philosophie: theoretische Entwürfe für praktische Legitimationsaufgaben fruchtbar zu machen. (shrink)

Two countable filters on ω are incompatible if they have no common infinite pseudointersection. Letting α(P f ) denote the minimal size of a maximal uncountable family of pairwise incompatible countable filters on ω, we prove the consistency of t $.

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.1 (2003) 13-31 [Access article in PDF] A Philosophical Inquiry into the Nature of Computer Art Holle Humphries Before the computer is accepted unquestioningly as a legitimate artistic medium, some of the challenging aesthetic and philosophical issues raised by [computer art] must be solved. The most haunting questions concern the impact of the technology on the artist, the creative process, and the nature of (...) art. 1How might we lead students in an exploration of the philosophical issues regarding art created with a computer? The most important step is first to guide them in exploring ontological concepts and questions asked about the nature of art and computer art, before investigating related issues of epistemology, value, and criticism. Students need to understand the nature of their art tool and medium of choice. Therefore, it becomes a matter of concern to discover that when discussing and writing about computer art, students sometimes use such terms interchangeably as "computer art" and "computer-generated art," when they are not synonymous, and talk about "virtual reality" as though engaging in any activity that involves a computer constitutes experiencing one. It is clear that this problem arises because many have not paused to examine the nature of computer art within the context of the process and product of art, and the subtle nuances regarding what might distinguish each from other human enterprise. To help clarify their thinking, we might use the foundation of art theory and the strategy of philosophical inquiry, implemented by adopting questioning strategies, to guide students through an exploration of the ontological nature of computer art. This can begin by launching the question: "What is the nature of art — or computer art?" Philosophy of Art: "What is the Nature of Art?" Many philosophers have attempted to describe or define the nature of art formulated in a theory of art. A theory of art attempts to specify where the essence of art is thought to reside, or what exactly art's essence is. [End Page 13]The imitation theory, initiated in the 5th century B.C. by Plato, held that to be a work of art, an object must mirror reality. 2 As this theory placed the essence of art in the objective properties of the art work itself, we consider the imitation theory to be object-centered or objective in nature. Similarly, with his formalist theory of art, Clive Bell claimed that the essence of art lies in the object — within the structural design properties of a work of art. To qualify as a work of art, an object must exhibit significant form. Significant form consists of certain formal properties such as the art elements of lines and color combined in a particular way according to art principles, all used to create certain forms and relations of forms. 3The expression theories of art shifted attention to the artist and audience and thus are considered subject centered, or subjective, bound up in notions of the experience of creation by the artist and/or the response of the audience. Benedetto Croce asserted that a work of art resides in the mind of the artist. An artist must experience an intuition, and it is this mental process that constitutes art, not the object which the artist might create thereafter. 4 Robin Collingwood claimed that art is an exploration, clarification, and expression of an artist's emotion, made clear to an audience through a medium. 5 Leo Tolstoy believed that art should be a vehicle by which the emotion experienced by the artist at the time of creation is transmitted to an audience, so that the audience can experience that emotion as well. 6Morris Weitz asserted that none of these theories capture an essence of art because they are either too broad, too narrow, or else are circular. He claimed that the concept of art cannot be limited to one essence delimited in a definition. Weitz suggested that we must instead look at what theories of art have to say is important about art so that we know what to... (shrink)

We consider the investigation of the embedding of semigroups in groups, a problem which spans the early-twentieth-century development of abstract algebra. Although this is a simple problem to state, it has proved rather harder to solve, and its apparent simplicity caused some of its would-be solvers to go awry. We begin with the analogous problem for rings, as dealt with by Ernst Steinitz, B. L. van der Waerden and Øystein Ore. After disposing of A. K. Sushkevich’s erroneous contribution in this (...) area, we present A. I. Maltsev’s example of a cancellative semigroup which may not be embedded in a group, which showed for the first time that such an embedding is not possible in general. We then look at the various conditions that were derived for such an embedding to take place: the sufficient conditions of Paul Dubreil and others, and the necessary and sufficient conditions obtained by A. I. Maltsev, Vlastimil Pták and Joachim Lambek. We conclude with some comments on the place of this problem within the theory of semigroups, and also within abstract algebra more generally. (shrink)

Between December 1855 and March 1856, a public dispute raged, in British national newspapers and locally published pamphlets, between two teachers at the University of Oxford: the mathematical lecturer Francis Ashpitel and Bartholomew Price, the professor of natural philosophy. The starting point for these exchanges was the particularly poor results that had come out of the final mathematics examinations in Oxford that December. Ashpitel, as one of the examiners, stood accused of setting questions that were too difficult for the ordinary (...) student, with the consequence that, in Price’s view, further mathematical study in Oxford – never as robust as in Cambridge – would be discouraged. We examine this short-lived affair, and use it not only to gain insight into the status of mathematical study in Oxford in the mid-nineteenth century, but also to point towards the increasing importance of competitive examinations in British public life at that time. (shrink)

In the history of mathematics, the algebraic theory of semigroups is a relative new-comer, with the theory proper developing only in the second half of the twentieth century. Before this, however, much groundwork was laid by researchers arriving at the study of semigroups from the directions of both group and ring theory. In this paper, we will trace some major strands in the early development of the algebraic theory of semigroups. We will begin with the aspects of the theory which (...) were directly inspired by, and were analogous to, existing results for both groups and rings, before moving on to consider the first independent theorems on semigroups: theorems with no group or ring analogues. (shrink)

We investigate uncountable maximal antichains of perfect trees and of splitting trees. We show that in the case of perfect trees they must have size of at least the dominating number, whereas for splitting trees they are of size at least \\), i.e. the covering coefficient of the meager ideal. Finally, we show that uncountable maximal antichains of superperfect trees are at least of size the bounding number; moreover we show that this is best possible.

Zusammenfassung: Seit Langem sieht die Welt sich wieder einer globalen pandemischen Bedrohung ausgesetzt, die nicht nur wissenschaftlich, wirtschaftlich, politisch und gesellschaftlich, sondern auch künstlerisch zu bewältigen versucht wird. Dabei dominieren vor allem zwei visuelle Phänomene die Bildwelten der journalistischen und sozialen Medien: das Bild der Maske und das Bild des Virus selbst. Beide Bilder sind insbesondere in der Verbindung mit epi- und pandemischer Erfahrung bereits hoch aufgeladen. Die Sichtbarkeit der Maske und die Sichtbarmachung des Virus verweisen auf ihre komplexen historischen (...) Dimensionen und rufen philosophisch-ethische Fragen auf. Durch eine Gegenüberstellung von künstlerischen Zeugnissen historischer und gegenwärtiger Seuchenerfahrung werden im vorliegenden Beitrag historisch tradierte Muster von narrativen und visuellen Seuchendarstellungen, die auch den gegenwärtigen Pandemiediskurs bestimmen, herausgearbeitet und kritisch hinterfragt. Dabei wird gefragt, wie Kunst und Literatur zu einer rhetorischen und metaphorischen Deeskalation aktueller und zukünftiger pandemischer Krisendiskurse beitragen und damit auch eine der Ästhetik inhärente Ethik aufzeigen können. (shrink)

Der Ruf des Esels als offenes Klangobjekt in Robert Bressons Film Au hazard Balthazar (F 1966), der die Bild-Montage insistierend stört, wird in diesem Beitrag in den Kontext der Bioakustik gestellt. Am JA des Esels differenzieren sich Geräusche medial so aus, dass die Grenze zwischen Ding und Kreatur durchlässig wird. Bressons Passion erweist sich damit als Experiment, die akustischen Kanäle der Kommunikation als Transformatoren von Lebewesen, Räumen und jener Übertragung wahrzunehmen, die kybernetisch informierten Tierforschern Sprache heißt. The paper presents the (...) donkey's bray in Robert Bresson's film (F 1966) that disturbs the montage insistently as an open sound object and puts it in the context of bioacoustics. The donkey's hee-haw diversifies noise in such a way that the borderline between object and creature becomes permeable. Bresson's passion proves to be an experiment to perceive the acoustic channels of communication as transformers of animals, spaces and that kind of transmission that researchers informed by cybernetics call »language«. (shrink)