We introduce the relation of almost-reduction in an arbitrary topological Ramsey space ℛ as a generalization of the relation of almost-inclusion on ℕ[∞]. This leads us to a type of ultrafilter [MATHEMATICAL SCRIPT CAPITAL U] ⊆ ℛ which corresponds to the well-known notion of selective ultrafilter on ℕ. The relationship turns out to be rather exact in the sense that it permits us to lift several well-known facts about selective ultrafilters on ℕ and the Ellentuck space (...) ℕ[∞] to the ultrafilter [MATHEMATICAL SCRIPT CAPITAL U] and the Ramsey space ℛ. For example, we prove that the open coloring axiom holds on L [[MATHEMATICAL SCRIPT CAPITAL U]], extending therefore the result from [3] which gives the same conclusion for the Ramsey space ℕ[∞]. (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)

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)

We study classes of ultrafilters on ω defined by a natural property of the Loeb measure in the Nonstandard Universe corresponding to the ultrafilter. This class, the Property M ultrafilters, is shown to contain all ultrafilters built up by taking iterated products over collections of pairwise nonisomorphic selective ultrafilters. Results on Property M ultrafilters are applied to the construction of extensions of probability measures, and to the study of measurable reductions between ultrafilters.

We study relations between measure-theoretic classes of ultrafilters, such as the Property M ultrafilters of [4], with other well-known ultrafilter classes. We define several classes of measure theoretic ultrafilters, of which the Property M ultrafilters are the strongest. We show which containments are provable in ZFC between these measure-theoretic ultrafilters and boolean combinations of well-known ultrafilters such as the selective, semi-selective, and P-point ultrafilters. We also list some of the containment results between measure-theoretic ultrafilters and several other (...) ultrafilter classes, such as the Arrow and Property C ultrafilters. (shrink)

We answer a question of Blass, Di Nasso, and Forti [2, 7] by proving, assuming Continuum Hypothesis or Martin’s Axiom, that there exists a P-point which is not interval-to-one and there exists an interval-to-one P-point which is neither quasi-selective nor weakly Ramsey.

We prove in set theory without the Axiom of Choice, that Rado’s selection lemma (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{RL}}$$\end{document}) implies the Hahn-Banach axiom. We also prove that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{RL}}$$\end{document} is equivalent to several consequences of the Tychonov theorem for compact Hausdorff spaces: in particular, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{RL}}$$\end{document} implies that every filter on a well orderable set is included in a (...) class='Hi'>ultrafilter. In set theory with atoms, the “Multiple Choice” axiom implies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{RL}}$$\end{document}. (shrink)

We study ultrafilters onω2produced by forcing with the quotient of${\cal P}$(ω2) by the Fubini square of the Fréchet filter onω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically (...) generated but that it shares with basically generated ultrafilters the property of not being at the top of the Tukey ordering. In fact, it is not Tukey-above [ω1]<ω, and it has only continuum many ultrafilters Tukey-below it. A tool in our proofs is the analysis of similar (but not the same) properties for ultrafilters obtained as the sum, over a selective ultrafilter, of nonisomorphic selective ultrafilters. (shrink)

A family \ is called Rosenthal if for every Boolean algebra \, bounded sequence \ of measures on \, antichain \ in \, and \, there exists \ such that \<\varepsilon \) for every \. Well-known and important Rosenthal’s lemma states that \ is a Rosenthal family. In this paper we provide a necessary condition in terms of antichains in \}\) for a family to be Rosenthal which leads us to a conclusion that no Rosenthal family has cardinality strictly less (...) than \\), the covering of category. We also study ultrafilters on \ which are Rosenthal families—we show that the class of Rosenthal ultrafilters contains all selective ultrafilters. (shrink)

There is an analogy between concepts such as end-extension types and minimal types in the model theory of Peano arithmetic and concepts such as P-points and selective ultrafilters in the theory of ultrafilters on N. Using the notion of conservative extensions of models, we prove some theorems clarifying the relation between these pairs of analogous concepts. We also use the analogy to obtain some model-theoretic results with techniques originally used in ultrafilter theory. These results assert that every countable (...) nonstandard model of arithmetic has a bounded minimal extension and that some types in arithmetic are not 2-isolated. (shrink)

We prove that for [Formula: see text] and [Formula: see text] there is a forcing extension with exactly n near-coherence classes of non-principal ultrafilters. We introduce localized versions of Matet forcing and we develop Ramsey spaces of names. The evaluation of some of the new forcings is based on a relative of Hindman’s theorem due to Blass 1987.

A P-point ultrafilter over \(\omega \) is called an interval P-point if for every function from \(\omega \) to \(\omega \) there exists a set _A_ in this ultrafilter such that the restriction of the function to _A_ is either a constant function or an interval-to-one function. In this paper we prove the following results. (1) Interval P-points are not isomorphism invariant under \(\textsf{CH}\) or \(\textsf{MA}\). (2) We identify a cardinal invariant \(\textbf{non}^{**}({\mathcal {I}}_{\tiny {\hbox {int}}})\) such that every (...) filter base of size less than continuum can be extended to an interval P-point if and only if \(\textbf{non}^{**}({\mathcal {I}}_{\tiny {\hbox {int}}})={\mathfrak {c}}\). (3) We prove the generic existence of slow/rapid non-interval P-points and slow/rapid interval P-points which are neither quasi-selective nor weakly Ramsey under the assumption \({\mathfrak {d}}={\mathfrak {c}}\) or \(\textbf{cov}({\mathcal {B}})={\mathfrak {c}}\). (shrink)

We continue the study of Rosenthal families initiated by Damian Sobota. We show that every Rosenthal filter is the intersection of a finite family of ultrafilters that are pairwise incomparable in the Rudin-Keisler partial ordering of ultrafilters. We introduce a property of filters, called an \-filter, properly between a selective filter and a \-filter. We prove that every \-ultrafilter is a Rosenthal family. We prove that it is consistent with ZFC to have uncountably many \-ultrafilters such that any (...) intersection of finitely many of them is a Rosenthal filter. (shrink)

This is a survey of theories of scientific method which opens the book "After Popper, Kuhn and Feyerabend: Recent Issues in Theories of Scientific Method".

Alasdair MacIntyre has written a selective history of the Catholic philosophical tradition, designed to show how belief in God informed and informs philosophical enquiry in different historical and social settings.

Ageing is associated with a decline in autophagy and elevated reactive oxygen species (ROS), which can breach the capacity of antioxidant systems. Resulting oxidative stress can cause further cellular damage, including DNA breaks and protein misfolding. This poses a challenge for longevous organisms, including humans. In this review, we hypothesise that in the course of human evolution selective autophagy receptors (SARs) acquired the ability to sense and respond to localised oxidative stress. We posit that in the vicinity of protein (...) aggregates and dysfunctional mitochondria oxidation of key cysteine residues in SARs induces their oligomerisation which initiates autophagy. The degradation of damaged cellular components thus could reduce ROS production and restore redox homeostasis. This evolutionarily acquired function of SARs may represent one of the biological adaptations that contributed to longer lifespan. Inversely, loss of this mechanism can lead to age‐related diseases associated with impaired autophagy and oxidative stress. (shrink)

The majority of evidence on social anxiety -linked attentional biases to threat comes from research using facial expressions. Emotions are, however, communicated through other channels, such as voice. Despite its importance in the interpretation of social cues, emotional prosody processing in SA has been barely explored. This study investigated whether SA is associated with enhanced processing of task-irrelevant angry prosody. Fifty-three participants with high and low SA performed a dichotic listening task in which pairs of male/female voices were presented, one (...) to each ear, with either the same or different prosody. Participants were instructed to focus on either the left or right ear and to identify the speaker’s gender in the attended side. Our main results show that, once attended, task-irrelevant angry prosody elicits greater interference than does neutral prosody. Surprisingly, high socially anxious participants were less prone to distraction from attended-angry prosody than were low socially anxious individuals. These findings emphasise the importance of examining SA-related biases across modalities. (shrink)

Realists have responded to challenges from the historical record of successful but ultimately rejected theories with what I call the selective confirmation strategy: arguing that only idle parts of past theories have been rejected, while truly success‐generating features have been confirmed by further inquiry. I argue first, that this strategy is unconvincing without some prospectively applicable criterion of idleness for theoretical posits, and second, that existing efforts to provide one either convict all theoretical posits of idleness (Kitcher) or stand (...) refuted by detailed consideration of the very examples (optical/electromagnetic ether, caloric fluid) to which they appeal (Psillos). I also argue that available avenues for improving on these proposals are unpromising. (shrink)

One of the popular realist responses to the pessimistic meta-induction is the ‘selective’ move, where a realist only commits to the ‘working posits’ of a successful theory, and withholds commitment to ‘idle posits’. Antirealists often criticise selective realists for not being able to articulate exactly what is meant by ‘working’ and/or not being able to identify the working posits except in hindsight. This paper aims to establish two results: sometimes a proposition is, in an important sense, ‘doing work’, (...) and yet does not warrant realist commitment, and the realist will be able to respond to PMI-style historical challenges if she can merely show that certain selected posits do not require realist commitment. These two results act to significantly adjust the dialectic vis-à-vis PMI-style challenges to selective realism. (shrink)

Liberty-restricting measures have been implemented for centuries to limit the spread of infectious diseases. This article considers if and when it may be ethically acceptable to impose selective liberty-restricting measures in order to reduce the negative impacts of a pandemic by preventing particularly vulnerable groups of the community from contracting the disease. We argue that the commonly accepted explanation—that liberty restrictions may be justified to prevent harm to others when this is the least restrictive option—fails to adequately accommodate the (...) complexity of the issue or the difficult choices that must be made, as illustrated by the COVID-19 pandemic. We introduce a dualist consequentialist approach, weighing utility at both a population and individual level, which may provide a better framework for considering the justification for liberty restrictions. While liberty-restricting measures may be justified on the basis of significant benefits to the population and small costs for overall utility to individuals, the question of whether it is acceptable to discriminate should be considered separately. This is because the consequentialist approach does not adequately account for the value of equality. This value may be protected through the application of an additional proportionality test. An algorithm for making decisions is proposed. Ultimately whether selective liberty-restricting measures are imposed will depend on a range of factors, including how widespread infection is in the community, the level of risk and harm a society is willing to accept, and the efficacy and cost of other mitigation options. (shrink)

With evidence of vaccine hesitancy in several jurisdictions, the option of making COVID-19 vaccination mandatory requires consideration. In this paper I argue that it would be ethical to make the COVID-19 vaccination mandatory for older people who are at highest risk of severe disease, but if this were to occur, and while there is limited knowledge of the disease and vaccines, there are not likely to be sufficient grounds to mandate vaccination for those at lower risk. Mandating vaccination for those (...) at high risk of severe disease is justified on the basis of the harm principle, as there is evidence that this would remove the grave public health threat of COVID-19. The risk–benefit profile of vaccination is also more clearly in the interests of those at highest risk, so mandatory vaccination entails a less severe cost to them. Therefore, a selective mandate would create fairness in the distribution of risks. The level of coercion imposed by a mandate would need to be proportionate, and it is likely that multiple approaches will be needed to increase vaccine uptake. However, a selective mandate for COVID-19 vaccines is likely to be an ethical choice and should be considered by policy-makers. (shrink)

This article presents an argument for the view that we can perceive temporal features without awareness. Evidence for this claim comes from recent empirical work on selective visual attention. An interpretation of selective attention as a mechanism that processes high-level perceptual features is offered and defended against one particular objection. In conclusion, time perception likely has an unconscious dimension and temporal mental qualities can be instantiated without ever being conscious.

.... The strategy I have defended involves drawing a distinction between those who can and cannot legitimately hold an agent responsible in circumstances when the agent is being covertly controlled (e.g. through implantation processes). What is intuitively unacceptable, I maintain, is that an agent should be held responsible or subject to reactive attitudes that come from another agent who is covertly controlling or manipulating him. This places some limits on who is entitled to take up the participant stance in relation (...) to agents who are rational self-controllers but nevertheless subject to covert control.26 In this way, what is compromised by conditions of covert control is not the responsibility of the agent as such. It is, rather, the participant stance of those other agents who covertly control him. Clearly it is possible to establish these specific limits on who can hold these agents responsible without denying that the agents themselves remain free and responsible. When we take this approach we will find that we are no longer faced with an unattractive choice between simply “biting the bullet” or having to “spit it out”. All we need to do is chew carefully, until there is nothing left that we find too hard to swallow. (shrink)

Many high-income countries have skill-selective immigration policies, favoring prospective immigrants who are highly skilled. I investigate whether it is permissible for high-income countries to adopt such policies. Adopting what Joseph Carens calls a " realistic approach " to the ethics of immigration, I argue first that it is in principle permissible for high-income countries to take skill as a consideration in favor of selecting one prospective immigrant rather than another. I argue second that high-income countries must ensure that their (...) skill-selective immigration policies do not contribute to the non-fulfillment of their duty to aid residents of low-and middle-income countries. (shrink)

Similar to parasites, malignant cells exploit the host for energy, resources and protection, thereby impairing host health and fitness. Although cancer is widespread in the animal kingdom, its impact on life history traits and strategies have rarely been documented. Devil facial tumour disease, a transmissible cancer, afflicting Tasmanian devils, provides an ideal model system to monitor the impact of cancer on host life-history, and to elucidate the evolutionary arms-race between malignant cells and their hosts. Here we provide an overview of (...) parasite-induced host life history adaptations, then both phenotypic plasticity of LH responses and changes in allele frequencies that affect LH traits of Tasmanian devils in response to DFTD are discussed. We conclude that akin to parasites, cancer can directly and indirectly affect devil LH traits and trigger host evolutionary responses. Consequently, it is important to consider oncogenic processes as a selective force in wildlife. Exposure to transmissible cancer cells, i.e., Tasmanian devil facial tumour cells, can cause changes to life history traits either as the result of phenotypic plasticity in response to exposure during the lifetime of the individual or as the result of evolutionary change in LH traits due to selection over generations.Photo credits: Frédéric Thomas, Sarah Peck, Geordie Jennings. (shrink)

My current opinion is that the selective realist is in a strong position vis-à-vis the historical challenges. Certainly the realist needs to invoke some careful criteria for realist commitment, and various nuances concerning the nature of her epistemic commitment, and this may raise the ‘death by a thousand qualifications’ question mark. But the concern is unfounded: the qualifications are all independently motivated, and indeed necessary given the philosophical complexity. Qualifications are to be welcomed here; often the truth is far (...) from simple! (shrink)

This book is the first full-length treatment of rational egoism, and it provides both a selective history of the subject as well as a philosophical analysis of the arguments that have been deployed in its defense.

In metaphysics, we seem to have in every generation an oscillation between realist positions and stances that are in one way or another idealist, instrumentalist, or constructivist. Realists in the philosophy of science are those philosophers who will not conclude, from the fact that scientific theories are undoubtedly constructs of human mentality and culture, that therefore the content of these theories is inevitably some function of the human mentality and culture that have produced them. Realists are unimpressed by response-dependence. Realism (...) is metaphysical optimism; it has not abandoned the notion that exercising our capacities does not disqualify us from discovery. (shrink)

Males are selectively afflicted with the neurodevelopmental and psychiatric disorders of childhood, a broad and virtually ubiquitous phenomenon that has not received proper attention in the biological study of sex differences. The previous literature has alluded to psychosocial differences, genetic factors and elements pertaining to male “complexity” and relative immaturity, but these are not deemed an adequate explanation for selective male affliction. The structure of sex differences in neurodevelopmental disorders is hypothesized to contain these elements: Males are more frequently (...) afflicted, females more severely; disorders arising in females are largely mediated by the genotype; in males, by a genotype by environment interaction; complications of pregnancy and delivery occur more frequently with male births; such complications are decisive and influence subsequent development. We hypothesize that there is something about the male fetus that evokes an inhospitable uterine environment. This “evocative principle” is hypothesized to relate to the relative antigenicity of the male fetus, which may induce a state of maternal immunoreactivity, leading either directly or indirectly to fetal damage. The immunoreactive theory thus constructed is borrowed from studies of sex ratios and is the only explanation consistent with negative parity effects in the occurrence of pregnancy complications and certain neurodevelopmental disorders. Although the theory is necessarily speculative, it is heuristic and hypotheses derived from it are proposed; some are confirmed in the existing literature and by the authors' research. (shrink)

At this stage of the COVID-19 pandemic, two policy aims are imperative: avoiding the need for a general lockdown of the population, with all its economic, social and health costs, and preventing the healthcare system from being overwhelmed by the unchecked spread of infection. Achieving these two aims requires the consideration of unpalatable measures. Julian Savulescu and James Cameron argue that mandatory isolation of the elderly is justified under these circumstances, as they are at increased risk of becoming severely ill (...) from COVID-19, and are thus likely to put disproportionate strain on limited healthcare resources. However, their arguments for this strategy are contingent on the lack of viable alternatives. We suggest that there is a possible alternative: a mandatory, centralised contact-tracing app. We argue that this strategy is ethically preferable to the selective isolation of the elderly, because it does not target members of a certain group, relying instead on the movements of each individual, and because it avoids the extended isolation of certain members of the society. Although this type of contact-tracing app has its drawbacks, we contend that this measure warrants serious consideration. (shrink)