We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semi-Cohen algebras, pseudo-Cohen algebras and potentially Cohen algebras. These classes of Boolean algebras are closed under completion.

This article investigates the weak distributivity of Boolean σ-algebras satisfying the countable chain condition. It addresses primarily the question when such algebras carry a σ-additive measure. We use as a starting point the problem of John von Neumann stated in 1937 in the Scottish Book. He asked if the countable chain condition and weak distributivity are sufficient for the existence of such a measure.Subsequent research has shown that the problem has two aspects: one set theoretic and one combinatorial. Recent results (...) provide a complete solution of both the set theoretic and the combinatorial problems. We shall survey the history of von Neumann's Problem and outline the solution of the set theoretic problem. The technique that we describe owes much to the early work of Dorothy Maharam to whom we dedicate this article.§1. Complete Boolean algebras and weak distributivity. ABoolean algebrais a setBwith Boolean operationsa˅b,a˄b and −a, partial orderinga≤bdefined bya˄b=aand the smallest and greatest element,0and1. By Stone's Representation Theorem, every Boolean algebra is isomorphic to an algebra of subsets of some nonempty setS, under operationsa∪b,a∩b,S−a, ordered by inclusion, with0= ∅ and1=S.Complete Boolean algebras and weak distributivity.A Boolean algebrais a setBwith Boolean operationsa˅b,a˄b and -a, partial orderinga≤bdefined bya˄b=aand the smallest and greatest element.0and1. By Stone's Representation Theorem, every Boolean algebra is isomorphic to an algebra of subsets of some nonempty setS, under operationsa∪b,a∩b,S-a, ordered by inclusion, with0= ϕ and1=S. (shrink)

In the previous paper of this volume, Kojman and Shelah solved our long standing problem of collapsing cardinal κ0 to ω1 by the forcing for singular κ with countable cofinality. The aim of the present paper is to give an explicit construction of the Boolean matrix for this collapse.

The widely accepted two-dimensional circumplex model of emotions posits that most instances of human emotional experience can be understood within the two general dimensions of valence and activation. Currently, this model is facing some criticism, because complex emotions in particular are hard to define within only these two general dimensions. The present theory-driven study introduces an innovative analytical approach working in a way other than the conventional, two-dimensional paradigm. The main goal was to map and project semantic emotion space in (...) terms of mutual positions of various emotion prototypical categories. Participants (N = 187; 54.5% females) judged 16 discrete emotions in terms of valence, intensity, controllability and utility. The results revealed that these four dimensional input measures were uncorrelated. This implies that valence, intensity, controllability and utility represented clearly different qualities of discrete emotions in the judgments of the participants. Based on this data, we constructed a 3D hypercube-projection and compared it with various two-dimensional projections. This contrasting enabled us to detect several sources of bias when working with the traditional, two-dimensional analytical approach. Contrasting two-dimensional and three-dimensional projections revealed that the 2D models provided biased insights about how emotions are conceptually related to one another along multiple dimensions. The results of the present study point out the reductionist nature of the two-dimensional paradigm in the psychological theory of emotions and challenge the widely accepted circumplex model. (shrink)

The main aims of this paper are to establish the position of evolutionary ontology within the Czech environmental debate, to identify why its untapped potential may be an inspiration in other social science disciplines and, finally, to suggest that evolutionary ontology be reconfigured in a particular way so that it can capitalize on its potential. A brief introduction outlines the context and the main ideas of evolutionary ontology and is followed by a discussion of its weaknesses: an emphasis on a (...) confrontational style in addressing other social science disciplines and ignoring the specific nature of the disciplines which represent the main target group of this theory. Consequently, I suggested three main changes as to how evolutionary ontology should be presented. (shrink)

Let ${\mathbb{B}}$ and ${\mathbb{C}}$ be Boolean algebras and ${e: \mathbb{B}\rightarrow \mathbb{C}}$ an embedding. We examine the hierarchy of ideals on ${\mathbb{C}}$ for which ${ \bar{e}: \mathbb{B}\rightarrow \mathbb{C} / \fancyscript{I}}$ is a regular (i.e. complete) embedding. As an application we deal with the interrelationship between ${\fancyscript{P}(\omega)/{{\rm fin}}}$ in the ground model and in its extension. If M is an extension of V containing a new subset of ω, then in M there is an almost disjoint refinement of the family ([ω]ω) V (...) . Moreover, there is, in M, exactly one ideal ${\fancyscript{I}}$ on ω such that ${(\fancyscript{P}(\omega)/{{\rm fin}})^V}$ is a dense subalgebra of ${(\fancyscript{P}(\omega)/\fancyscript{I})^M}$ if and only if M does not contain an independent (splitting) real. We show that for a generic extension V[G], the canonical embedding $$\fancyscript{P}^V(\omega){/}{\rm fin}\hookrightarrow \fancyscript{P}(\omega){/}(U(Os)(\mathbb{B}))^G$$ is a regular one, where ${U(Os)(\mathbb{B})}$ is the Urysohn closure of the zero-convergence structure on ${\mathbb{B}}$. (shrink)

Claude Rolley, Juliette Langlois, Nathalie Balcar και Martine Regert Από την άσφαλτο στη ρητίνη : το γέμισμα του αυτιού ενός γρύπα από τους Δελφούς σ. 55-65 Το γέμισμα του κενού στο αυτί μιας σφυρήλατης προτομής γρύπα από τους Δελφούς έγινε με άσφαλτο. Ένα ακόμη επιχείρημα για την προέλευση κατασκευής από την Εγγύς Ανατολή των σφυρήλατων προτομών των στερεωμένων στους λέβητες που βρέθηκαν στην Ελλάδα και την Ετρουρία.

This article deals primarily with the examination of two key and exegetically demanding expressions in the text of the General Epistle of James, which relate to fundamental biblical principles on planning the future of the believer and reconciling human life with God’s will expressed in Holy Scripture. The first one is the hapax legomenon Ἄγε νῦν, the significance of which is closely related to updating of the affected principles with practice. The second term is ποιήσοµεν, which, in most translations, translates (...) as ‘remain’ and does not reflect the core idea of the examined verse. We prove that a more authentic and appropriate translation is ‘work’. Our aim was to find out what new interpretive possibilities the original biblical text offers. The constitutive starting point for research is Novum Testamentum Graecum – Editio Critica Maior. We then compared these texts with the Slovak Ecumenical Bible. The method of our exegetical work was not primarily comparison, but a linguistic analysis and historical-critical exegesis, the result of which is a completely new proposal for the translation of the scrutinised texts. Auxiliary materials were the most important patristic and exegetical commentaries. In conclusion, we state that the analysis made it possible to find a new translation of the researched text, which can really contribute to the improvement of further review and publication of the ecumenical translation of the Bible into various languages.Contribution: The article examines the source Greek biblical text of James 4:13–15 and reveals a new interpretation of it. This interpretation brings a new, biblical light into the field of planning, which is one of the most current topics nowadays. With its content and especially its conclusions, it contributes to the goals of this theological journal, the subject of which is also the research of Greek biblical manuscripts. (shrink)

While the emancipatory efforts of the Czech national revival culminated at the end of the 18th and in the 19th century, manifestations of national feeling in the 17th century Czech Lands were rather rare. The article focuses on the concept of nationality as it was treated by scholars from the monastic orders such as the German provincial of the Czech Franciscan province, Bernhard Sannig (1637–1704), or the Czech Jesuit Bohuslav Balbín (1621–1688), whose views are briefly compared with those of (...) the most significant representative of the Czech Protestant emigration – Johann Amos Comenius (1592–1670). By the means of analysis and comparison of several texts, the article investigates how the concept of nationality was gradually rationalized and moralized through the ethical categories of vice and virtue. These reflections on nation, nationality, and patriotism and their moral assessment demonstrate that their authors anticipated some elements of the later formulated doctrine of the natural law of nations, which theoretically justified the demands of the Czech national revival and formed the basis for the concept of Czech history. (shrink)

We investigate cardinal invariants related to the structure of dense sets of rationals modulo the nowhere dense sets. We prove that , thus dualizing the already known [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. Math. 183 59–80, Theorem 3.6]. We also show the consistency of each of and . Our results answer four questions of Balcar, Hernández and Hrušák [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the (...) rationals, Fund. Math. 183 59–80, Questions 3.11]. (shrink)

We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra contains a complete subalgebra which is isomorphic to the collapse algebra CompCol. Consequently, adding a generic filter to the quotient algebra collapses μ0 to 1. Another corollary is that the Baire number of the space U of all uniform ultrafilters over μ is equal to ω2. The corollaries affirm two conjectures of Balcar and Simon. The proof uses pcf theory.

We study some properties of the quotient forcing notions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{tr(I)} = \wp(2^{< \omega})/tr(i)}$$\end{document} and PI = B(2ω)/I in two special cases: when I is the σ-ideal of meager sets or the σ-ideal of null sets on 2ω. We show that the remainder forcing RI = Qtr(I)/PI is σ-closed in these cases. We also study the cardinal invariant of the continuum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{h}_{\mathbb{Q}}}$$\end{document}, the distributivity (...) number of the quotient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Dense(\mathbb{Q})/nwd}$$\end{document}, in order to show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\wp(\mathbb{Q})/nwd}$$\end{document} collapses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{h}_{\mathbb{Q}}}$$\end{document}, thus answering a question addressed in Balcar et al. (Fundamenta Mathematicae 183:59–80, 2004). (shrink)

This article traces the life of Russian chemist Dmitri Mendeleev from childhood in Siberia, through education and training to become the first formulator of the Periodic Table, the logo of chemistry. His unique contribution is described and analysed; what factors helped him be the first formulator? What did he do after making his most famous discovery? In addition the article peeps into his personal life, his dealings with his family and the authorities. Finally we look at honours he received in (...) later life. (shrink)