On a problem of P(α, δ, π) concerning generalized Alexandroff s cube

Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ), .Assuming that P (, , ) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, , ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, , ) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , , such that P (, , ) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (, ₁, 2 ) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.     

Disturbances of consciousness in dementia with Lewy bodies associated with alteration in nicotinic receptor binding in the temporal cortex

Disturbances of consciousness, including fluctuations in attention and awareness, are a common and clinically important symptom in dementia with Lewy bodies (DLB). In the present study we investigate potential mechanisms of such disturbances of consciousness (DOC) in a clinicopathological study evaluating specific components of the cholinergic system. [3H]Epibatidine binding to the high-affinity nicotinic receptor in the temporal cortex (Brodmann's areas 20 and 36) differentiated DLB cases with and without DOC, being 62-66% higher in those with DOC (F=4.5,p=.025). The were no differences between DLB patients with or without DOC in 125I-labeled alpha-bungaratoxin binding to the low-affinity nicotinic receptor, [3H]pirenzepine binding to the muscarinic M1 receptor, or in choline acetyltransferase activity. These findings provide support for the hypothesis that cholinergic activity is an important neural correlate if consciousness and suggest a mechanism of DOC in DLB involving alterations in the nicotinic receptor, composed of predominantly alpha4 and beta2 subunits.     

Spontaneous adaptation explains why people act faster when being imitated

The human ability to perform joint actions is often attributed to high-level cognitive processes. For example, the finding that action leaders act faster when imitated by their partners has been interpreted as evidence for anticipation of the other’s actions (Pfister, Dignath, Hommel, & Kunde, 2013). In two experiments, we showed that a low-level mechanism can account for this finding. Action leaders were faster when imitated than when counterimitated, but only if they could observe their partner’s actions (Exp. 1). Crucially, when due to our manipulation the partner’s imitative actions became slower than the counterimitative actions, leaders also became slower when they were imitated, and faster when counterimitated (Exp. 2). Our results suggest that spontaneous temporal adaptation is a key mechanism in joint action tasks. We argue for a reconsideration of other phenomena that have traditionally been attributed solely to high-level processes.     

Agency,communion and entitlement

In this study, the relationship between agency, communion, and the active, passive, and revenge forms of entitlement is examined. Results indicate that active entitlement was positively related to agency, negatively to communion (Study 1), and unrelated to unmitigated agency and communion (Study 2). Passive entitlement was positively related to communion (in regular and unmitigated forms) and negatively related to agency (in both forms). Revenge entitlement was positively related to agency (unmitigated and regular), and negatively related to both regular and unmitigated communal orientations. Detected relationships were independent from self‐esteem (Study 1). The findings are discussed in relation to distinctions between narcissistic and healthy entitlement, and within the context of the three‐dimensional model of entitlement.     

On decidable consequence operators

The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.     

“Interest in the service of that which is disinterested.” Józef Tischner’s anthropologico-ethical project of work

This paper focuses on one of Tischner’s last and little-known essays on the issues concerning work in the era of free market and the hegemony of the laws of economic calculation. In a discussion with Dominique Méda and André Gorz, Tischner diagnoses various threats to contemporary forms of work. Tischner criticizes above all the one-sided—that is, only objective—conception of today’s work. Referring to his own and original anthropologico-ethical project of work, the Polish scholar draws the reader’s attention to the need to promote the subjective model of work to be construed as interhuman dialogue. In work, thus construed, Tischner discerns a guarantee of the moral order of contemporary societies. His anthropological-ethical concept of work successfully inscribes itself in some of the models of work of the future, which are very much promoted today.

     

Generalization of Scott's formula for retractions from generalized Alexandroff's cube

In the paper [2] the following theorem is shown: Theorem (Th. 3,5, [2]), If α=0 or δ=∞ or α?δ, then a closure space X is an absolute extensor for the category of 〈α, δ〉 -closure spaces iff a contraction of X is the closure space of all 〈α, δ〉-filters in an 〈α, δ〉-semidistributive lattice. In the case when α=ω and δ=∞, this theorem becomes Scott's theorem: Theorem ([7]). A topological space X is an absolute extensor for the category of all topological spaces iff a contraction of X is a topological space of “Scott's open sets” in a continuous lattice. On the other hand, when α=0 and δ=ω, this theorem becomes Jankowski's theorem: Theorem ([4]). A closure space X is an absolute extensor for the category of all closure spaces satisfying the compactness theorem iff a contraction of X is a closure space of all filters in a complete Heyting lattice. But for separate cases of α and δ, the Theorem 3.5 from [2] is proved using essentialy different methods. In this paper it is shown that this theorem can be proved using, for retraction, one uniform formula. Namely it is proved that if α= 0 or δ= ∞ or α ? δ and \(F_{\alpha ,\delta } \left( L \right) \subseteq B_{\alpha ,\delta }^\mathfrak{n} \) and if L is an 〈α, δ〉-semidistributive lattice, then the function $$r:{\text{ }}B_{\alpha ,\delta }^\mathfrak{n} \to F_{\alpha ,\delta } \left( L \right)$$ such that for x ε ? ( \(\mathfrak{n}\) ): (*) $$r\left( x \right) = inf_L \left\{ {l \in L|\left( {\forall A \subseteq L} \right)x \in C\left( A \right) \Rightarrow l \in C\left( A \right)} \right\}$$ defines retraction, where C is a proper closure operator for \(B_{\alpha ,\delta }^\mathfrak{n} \) . It is also proved that the formula (*) defines retraction for all 〈α, δ〉, whenever L is an 〈α, δ〉 -pseudodistributive lattice. Moreover it is proved that when α=ω and δ=∞, the formula (*) defines identical retraction to the formula given in [7], and when α = 0 and δ=ω, the formula (*) defines identical retraction to the formula given in [4].     

From the Profession

Studies in East European Thought -     

Belief in a zero-sum game and subjective well-being across 35 countries

Current Psychology - This article presents a short research report on the relationship between perceived antagonism in social relations measured using the Belief in a Zero-Sum Game (BZSG) scale,...     

Human Health and Christianity in the Context of the Dilemma of Forgiveness

Journal of Religion and Health - This article argues that Christianity has the potential to strengthen people’s health when solving the forgiveness dilemma....