Let X be an infinite set and let and denote the propositions “every filter on X can be extended to an ultrafilter” and “X has a free ultrafilter”, respectively. We denote by the Stone space of the Boolean algebra of all subsets of X. We show: For every well‐ordered cardinal number ℵ, (ℵ) iff (2ℵ). iff “ is a continuous image of ” iff “ has a free open ultrafilter ” iff “every countably infinite subset (...) of has a limit point”. implies “every open filter on extends to an open ultrafilter” implies “has an open ultrafilter” implies It is relatively consistent with that (ω) holds, whereas (ω) fails. In particular, none of the statements given in (2) implies (ω). (shrink)

An analogue of Mathias forcing is studied in connection of free Boolean algebras and nowhere dense ultrafilters. Some applications to rigid Boolean algebras are given.

A free ultrafilter $\mathcal{U}$ on $\omega$ is called a $T$-point if, for every countable group $G$ of permutations of $\omega$, there exists $U\in\mathcal{U}$ such that, for each $g\in G$, the set $\{x\in U:gx\ne x, gx\in U\}$ is finite. We show that each $P$-point and each $Q$-point in $\omega^*$ is a $T$-point, and, under CH, construct a $T$-point, which is neither a $P$-point, nor a $Q$-point. A question whether $T$-points exist in ZFC is open.

The interplay between ultrafilters and unbounded subsets of \ with the order \ of strict eventual domination is studied. Among the tools are special kinds of non-principal ultrafilters on \. These include simple P-points; that is, ultrafilters with a base that is well-ordered with respect to the reverse of the order \ of almost inclusion. It is shown that the cofinality of such a base must be either \, the least cardinality of \-unbounded set, or \, the least cardinality of (...) a \-cofinal set. The small uncountable cardinal \ is introduced. Consequences of \ and of \ are explored; in particular, both imply \. Here \ is the reaping number, and is also the least cardinality of a \-base for a free ultrafilter. Both of these inequalities are shown to occur if there exist simple P-points of different cofinalities and there exist simple \-points and \-points), but this is a long-standing open problem. Six axioms on nonprincipal ultrafilters on \ and the relationships between them are discussed along with various models of set theory in which one or more are known to hold. The strongest of these, Axiom 1, is that for every free ultrafilter \ and for every \-unbounded \-chain C of increasing functions in \, C is also unbounded in the ultraproduct \. The other axioms replace one or both quantifiers with “there exists.” The negation of Axiom 3 in a model provides a family of normal sequentially compact spaces whose product is not countably compact. The question of whether such a family exists in ZFC, even with “normal” weakened to “regular”, is a famous unsolved problem of set-theoretic topology, known as the Scarborough–Stone problem. (shrink)

In this article we, given a free ultrafilter p on ω, consider the following classes of ultrafilters:(1) T(p) - the set of ultrafilters Rudin-Keisler equivalent to p,(2) S(p)={q ∈ ω*:∃ f ∈ ω ω , strictly increasing, such that q=f β (p)},(3) I(p) - the set of strong Rudin-Blass predecessors of p,(4) R(p) - the set of ultrafilters equivalent to p in the strong Rudin-Blass order,(5) P RB (p) - the set of Rudin-Blass predecessors of p, and(6) P (...) RK (p) - the set of Rudin-Keisler predecessors of p,and analyze relationships between them. We introduce the semi-P-points as those ultrafilters p ∈ ω* for which P RB (p)=P RK (p), and investigate their relations with P-points, weak-P-points and Q-points. In particular, we prove that for every semi-P-point p its α-th left power α p is a semi-P-point, and we prove that non-semi-P-points exist in ZFC. Further, we define an order ⊴ in T(p) by r⊴q if and only if r ∈ S(q). We prove that (S(p),⊴) is always downwards directed, (R(p),⊴) is always downwards and upwards directed, and (T(p),⊴) is linear if and only if p is selective.We also characterize rapid ultrafilters as those ultrafilters p ∈ ω* for which R(p)∖S(p) is a dense subset of ω*.A space X is M-pseudocompact (for ) if for every sequence (U n ) n < ω of disjoint open subsets of X, there are q ∈ M and x ∈ X such that x=q-lim (U n ); that is, for every neighborhood V of x. The P RK (p)-pseudocompact spaces were studied in [ST].In this article we analyze M-pseudocompactness when M is one of the classes S(p), R(p), T(p), I(p), P RB (p) and P RK (p). We prove that every Frolik space is S(p)-pseudocompact for every p ∈ ω*, and determine when a subspace with is M-pseudocompact. (shrink)

Let G be a group, and let X be an infinite transitive G-space. A free ultrafilter U on X is called G-selective if, for any G-invariant partition P of X, either one cell of P is a member of U, or there is a member of U which meets each cell of P in at most one point. We show that in ZFC with no additional set-theoretical assumptions there exists a G-selective ultrafilter on X. We describe all (...) G-spaces X such that each free ultrafilter on X is G-selective, and we prove that a free ultrafilter U on ω is selective if and only if U is G-selective with respect to the action of any countable group G of permutations of ω. A free ultrafilter U on X is called G-Ramsey if, for any G-invariant coloring χ:[X]2→{0,1}, there is U∈U such that [U]2 is χ-monochromatic. We show that each G-Ramsey ultrafilter on X is G-selective. Additional theorems give a lot of examples of ultrafilters on Z that are Z-selective but not Z-Ramsey. (shrink)

It is well known that, in a topological space, the open sets can be characterized using ?lter convergence. In ZF , we cannot replace filters by ultrafilters. It is proven that the ultra?lter convergence determines the open sets for every topological space if and only if the Ultrafilter Theorem holds. More, we can also prove that the Ultra?lter Theorem is equivalent to the fact that uX = kX for every topological space X, where k is the usual Kuratowski closure (...) operator and u is the Ultra?lter Closure with uX := {x ∈ X: [U converges to x and A ∈ U ]}. However, it is possible to built a topological space X for which uX ≠ kX, but the open sets are characterized by the ultra?lter convergence. To do so, it is proved that if every set has a free ultra?lter, then the Axiom of Countable Choice holds for families of non-empty finite sets. It is also investigated under which set theoretic conditions the equality u = k is true in some subclasses of topological spaces, such as metric spaces, second countable T0-spaces or {ℝ}. (shrink)

In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we show (...) that Grzegorczyk points are maximal contracting filters in the sense of De Vries, but the converse inclusion is not necessarily true. We also compare the notions of a Grzegorczyk point and an ultrafilter, and establish several properties of topological spaces based on Grzegorczyk structures. The main results of the paper are representation and completion theorems for G-structures. We prove both set-theoretical and topological representation theorems for various classes of G-structures. We also present topological object duality theorem for the class of complete G-structures and the class of concentric spaces, both restricted to structures which satisfy countable chain condition. We conclude the paper with proving equivalence of the original Grzegorczyk axiom with the one accepted by us as axiom. (shrink)

For much of the last 50 years, a key platform animating public sector reform in Canada and elsewhere has been that efficiency and effectiveness can be achieved by adapting private sector financial management methods and practices. We argue that the recent re-establishment of the Office of the Comptroller General (OCG) of Canada represents a key element of a program of strengthening financial accountability that has emerged within the Canadian Federal Government. Although this program is longstanding and is associated Canada’s implementation (...) of new public management initiatives, it has recently drawn particular sustenance from the sponsorship scandal in Canada. We demonstrate that the reincarnated OCG, re-established amid a rhetoric of “modernization” and of “strengthening” accountability, has a wide-ranging mandate to enhance financial and audit controls, create financial standards, nurture professional development, and oversee government spending. We explore some of the consequences of this development and of the broader financial accountability mechanisms introduced in response to the Sponsorship scandal within the Canadian public sector. (shrink)

The aim of UK-REACH (“The United Kingdom Research study into Ethnicity And COVID-19 outcomes in Healthcare workers”) is to understand if, how, and why healthcare workers (HCWs) in the United Kingdom (UK) from ethnic minority groups are at increased risk of poor outcomes from COVID-19. In this article, we present findings from the ethical and legal stream of the study, which undertook qualitative research seeking to understand and address legal, ethical, and social acceptability issues around data protection, privacy, and information (...) governance associated with the linkage of HCWs’ registration data and healthcare data. We interviewed 22 key opinion leaders in healthcare and health research from across the UK in two-to-one semi-structured interviews. Transcripts were coded using qualitative thematic analysis. Participants told us that a significant aspect of Big Data research in public health is varying drivers of mistrust—of the research itself, research staff and funders, and broader concerns of mistrust within participant communities, particularly in the context of COVID-19 and those situated in more marginalised community settings. However, despite the challenges, participants also identified ways in which legally compliant and ethically informed approaches to research can be crafted to mitigate or overcome mistrust and establish greater confidence in Big Data public health research. Overall, our research indicates that a “Big Data Ethics by Design” approach to research in this area can help assure (1) that meaningful community and participant engagement is taking place and that extant challenges are addressed, and (2) that any new challenges or hitherto unknown unknowns can be rapidly and properly considered to ensure potential (but material) harms are identified and minimised where necessary. Our findings indicate such an approach, in turn, will help drive better scientific breakthroughs that translate into medical innovations and effective public health interventions, which benefit the publics studied, including those who are often marginalised in research. (shrink)

Name der Zeitschrift: Klio Jahrgang: 99 Heft: 2 Seiten: 586-628.

Many jurisdictions have put regulatory strategies in place to provide incentives and safeguards to whistleblowers to encourage whistleblowing on corporate wrongdoings. One such strategy is the provision of a financial incentive to the whistleblower if the complaint leads to a successful regulatory enforcement action against the offending organization. We conducted an experiment using professional accountants as participants to examine whether such an incentive encourages potential whistleblowers to report an observed financial reporting fraud to a relevant external authority. We also examine (...) the effect of perceived seriousness of the wrongdoing on accountants’ intention to whistleblow. We find that a financial incentive results in a higher intention to whistleblow to a relevant external authority. We also find that perceptions of the seriousness of the wrongdoing are significantly and positively associated with accountants’ intention to whistleblow to a relevant external authority. We find a significant interaction between the provision of a financial incentive and the perceived seriousness of the wrongdoing on the intention to report the wrongdoing externally. The intention to report the financial reporting fraud externally is higher when the level of perceived seriousness is higher, regardless of the availability of a financial incentive. However, when the perceived level of seriousness is lower, the presence of financial incentive results in a higher intention to report the financial reporting fraud externally. These findings indicate that the impact of a financial incentive on the intention to whistleblow is moderated by perceptions of the seriousness of the wrongdoing. (shrink)

Technology used in online marketing has advanced to a state where collection, enhancement and aggregation of information are instantaneous. This proliferation of customer information focused technology brings with it a host of issues surrounding customer privacy. This article makes two key contributions to the debate concerning digital privacy. First, we use theories of justice to help understand the way consumers conceive of, and react to, privacy concerns. Specifically, it is argued that an important component of consumers' privacy concerns relates to (...) fairness judgments, which in turn comprise of the two primary components of distributive and procedural justice. Second, we make a number of prescriptions, aimed at both firms and regulators, based on the notion that consumers respond to perceived privacy violations in much the same way they would respond to an unfair exchange. (shrink)

This paper investigates the key drivers behind the origins of value-for-money (VFM) audit in Canada and the aims, intents, and logics ascribed by the original proponents. Drawing on insights from governmentality and New Public Management, the paper utilizes analysis methods adapted from case study research to review a wide range of primary documentation (e.g., Hansards from the Public Accounts Committee, House of Commons debates, the so-called Wilson report and the FMCS study) and secondary documentation (newspaper articles, Office of the Auditor (...) General internal publications, journal articles). Major findings indicate a rise of a management consulting culture within the Auditor General’s office following the appointment of James Johnson Macdonell. VFM legislation effectively operationalized practices drawn from management consulting expertise by invitation of the consultant. It was offered as an answer to the growing scope and size of government, which had become problematized by the Auditor General in terms of parliament losing control over the public purse. The Auditor General’s invocation of financial crisis led to a substantial broadening of mandate and increase in resources for that office. (shrink)

The fungal cell wall is a dynamic structure that protects the cell from changes in osmotic pressure and other environmental stresses, while allowing the fungal cell to interact with its environment. The structure and biosynthesis of a fungal cell wall is unique to the fungi, and is therefore an excellent target for the development of anti‐fungal drugs. The structure of the fungal cell wall and the drugs that target its biosynthesis are reviewed. Based on studies in a number of fungi, (...) the cell wall has been shown to be primarily composed of chitin, glucans, mannans and glycoproteins. The biosynthesis of the various components of the fungal cell wall and the importance of the components in the formation of a functional cell wall, as revealed through mutational analyses, are discussed. There is strong evidence that the chitin, glucans and glycoproteins are covalently cross‐linked together and that the cross‐linking is a dynamic process that occurs extracellularly. BioEssays 28: 799–808, 2006. © 2006 Wiley Periodicals, Inc. (shrink)

Technology used in online marketing has advanced to a state where collection, enhancement and aggregation of information are instantaneous. This proliferation of customer information focused technology brings with it a host of issues surrounding customer privacy. This article makes two key contributions to the debate concerning digital privacy. First, we use theories of justice to help understand the way consumers conceive of, and react to, privacy concerns. Specifically, it is argued that an important component of consumers’ privacy concerns relates to (...) fairness judgments, which in turn comprise of the two primary components of distributive and procedural justice. Second, we make a number of prescriptions, aimed at both firms and regulators, based on the notion that consumers respond to perceived privacy violations in much the same way they would respond to an unfair exchange. (shrink)

Following Lauwers and Van Liedekerke (1995), this paper explores in a model-theoretic framework the relation between Arrovian aggregation rules and ultraproducts, in order to investigate a source of impossibility results for the case of an infinite number of individuals and an aggregation rule based on a free ultrafilter of decisive coalitions.

Applying Weglorz' mode s of set theory without the axiom of choice, we investigate Arrow-type social we fare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying “finite discrimination”, if and only if in Weglorz' mode there is a free ultrafilter on a set representing the individuals.