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)

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)

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.

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)

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.

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.

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 ${\mathfrak{P}{(\omega)}/{\rm fin}}$.

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 $.

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 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.

We prove that every analytic set in ω ω × ω ω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set, and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective.

We investigate the covering numbers of some ideals on $${^{\omega }}{2}{}$$ ω 2 associated with tree forcings. We prove that the covering of the Sacks ideal remains small in the Silver and uniform Sacks model, respectively, and that the coverings of the uniform Sacks ideal and the Mycielski ideal, $${\mathfrak {C}_{2}}$$ C 2, remain small in the Sacks model.

We investigate measure and category in the projective hierarchie in the presence of large cardinals. Assuming a measurable larger than $n$ Woodin cardinals we construct a model where every $\Delta ^1_{n+4}$ -set is measurable, but some $\Delta ^1_{n+4}$ -set does not have Baire property. Moreover, from the same assumption plus a precipitous ideal on $\omega _1$ we show how a model can be forced where every $\Sigma ^1_{n+4}-$ set is measurable and has Baire property.

Wearable robots are an emerging form of technology that allow organizations to combine the strength, precision, and performance of machines with the flexibility, intelligence, and problem-solving abilities of human wearers. Active exoskeletons are a type of wearable robot that gives wearers the ability to effortlessly lift up to 200 lbs., as well as perform other types of physically demanding tasks that would be too strenuous for most humans. Synchronization between exoskeleton suits and wearers is one of the most challenging requirements (...) to operate these technologies effectively. In this conceptual paper, we extend interpersonal adaption theory (IAT) to the exoskeleton context and explicate (a) the antecedents that are most likely to shape synchrony in human-exoskeleton interactions, (b) automatic and strategic synchrony as adaptive behaviors in human-exoskeleton interactions, and (c) outcome variables that are especially important in these processes. Lastly, we offer a discussion of key methodological challenges for measuring synchrony in human-exoskeleton interactions and offer a future research agenda for this important area. (shrink)

We investigate several versions of a cardinal characteristic $ \frak f$ defined by Frankiewicz. Vojtáš showed ${\frak b} \leq{\frak f}$ , and Blass showed ${\frak f} \leq \min({\frak d},{\mbox{\rm unif}}({\bf K}))$ . We show that all the versions coincide and that ${\frak f}$ is greater than or equal to the splitting number. We prove the consistency of $\max({\frak b},{\frak s}) <{\frak f}$ and of ${\frak f} < \min({\frak d},{\mbox{\rm unif}}({\bf K}))$.

Ayant depuis son premier livre exploré son hypothèse d'une naissance de notre langage articulé, humain, à partir de l'expérience de la mort d'autrui comme autre soi-même, Gérard Bucher expose dans un dernier ouvrage les raisons des travaux d'une vie entière. La poésie, pour Bucher, c'est ce qui reste (et qui, ainsi, nous est légué, génération après génération), d'une scène (ou archiscène) au cours de laquelle rien de moins que les clés de notre humanité nous sont données. Dans Homo (...) divinans, complété et relu avant sa disparition fin 2018, le philosophe nous propose les raisons pour lesquelles la poésie demeure notre avenir, dans et malgré nos temps difficultueux."--Page 4 of cover. (shrink)

How to create stunning black and white photos in a digital format Shooting pictures in black and white presents unique challenges for beginners and experienced digital photographers alike. A strong understanding of photography’s fundamentals is crucial to capturing great black and white images, and factors such as contrast and lighting are much more integral to black and white photography than to color. Black and White Digital Photography Photo Workshop teaches digital photographers the skills they need to master black and white (...) photography. Focuses on the rules of photography and how they apply differently to black and white photography Offers guidance for properly uploading digital images to a computer Explains insider tips and tricks for using Photoshop and Lightroom to successfully enhance black and white images Black and white photography presents different challenges than color photography. In Black and White Digital Photography Photo Workshop, photographers learn how to identify great opportunities for black and white photographs and how to turn those opportunities into stunning monochrome images they can be proud to display. (shrink)

Verträgt sich Religion mit Aufklärung? Was für eine Rolle spielt die Theologie dabei? Kants Der Streit der Fakultäten kommt zu dem Schluss, dass der unendliche Streit um die Religion nicht zwangsläufig zum Problem für die Aufklärung werden muss, sondern seine Institutionalisierung die beste Hoffnung für Freiheit ist: Ohne Kritik kein Fortschritt, ohne Streit bloß Irrglaube. F.W.J. Schellings, Jacques Derridas und Judith Butlers Auseinandersetzung mit Kants Werk zeigen jedoch auch, dass dabei auch die Regeln des Streites strittig werden müssen: Wer legt (...) die Regeln fest? So wird die Kritik an Religion selbst zwangsläufig mit Kritik konfrontiert: Wer hat die Macht über den vernünftigen Diskurs? Eine antagonismustheoretische Perspektive auf dieses Problem zeigt: Aus Feinden können Gegner werden und aus Krieg Streit. Doch ob sich Fortschritt und Freiheit aus braven Debatten und Reformen oder als harter Kampf einstellt - oder eben überhaupt nicht - ist eine offene Frage. (shrink)

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