On March 23rd, 2020, elite soccer academies in the UK closed in compliance with the government enforced lockdown intended to contain the COVID-19 pandemic. This forced parents, players, and coaches to reconsider how they interacted with, and supported, one another. The aims of the present study were to explore the perceptions of players, parents, and coaches regarding how they interacted and collaborated with one another during the COVID-19 pandemic to support wellbeing and performance, and; to identify opportunities to enhance workings (...) of those within the athletic triangle resulting from adaptions made following enforced lockdown. Using an interpretive description methodology, semi-structured interviews were conducted with five coaches, six players, and six parents from an English elite academy soccer club. Interviews were analyzed using thematic analysis. Findings highlighted the importance of support and the different means of communication used between members of the athletic triangle to facilitate such support; the increased understanding of each member of the athletic triangle, leading to enhanced relationships, and; how members of the athletic triangle adapted practice to facilitate relationship development during the pandemic and beyond. The identification of these considerations has implications for coach and parent education initiatives to allow for optimal functioning of the athletic triangle as elite academy soccer clubs return from lockdown. These include the importance of continued communication between coach, athlete and parent; increasing understanding of each individual within the athletic triangle; and utilizing key interpersonal and technological skills learnt during the lockdown to further facilitate engagement within the athletic triangle. (shrink)

In this paper, we give an example of a complete computable infinitary theory T with countable models ${\mathcal{M}}$ and ${\mathcal{N}}$ , where ${\mathcal{N}}$ is a proper computable infinitary extension of ${\mathcal{M}}$ and T has no uncountable model. In fact, ${\mathcal{M}}$ and ${\mathcal{N}}$ are (up to isomorphism) the only models of T. Moreover, for all computable ordinals α, the computable ${\Sigma_\alpha}$ part of T is hyperarithmetical. It follows from a theorem of Gregory (JSL 38:460–470, 1972; Not Am Math Soc 17:967–968, 1970) (...) that if T is a Π 1 1 set of computable infinitary sentences and T has a pair of models ${\mathcal{M}}$ and ${\mathcal{N}}$ , where ${\mathcal{N}}$ is a proper computable infinitary extension of ${\mathcal{M}}$ , then T would have an uncountable model. (shrink)

Here we prove that if T and T′ are strongly minimal theories, where T′ satisfies a certain property related to triviality and T does not, and T′ is model complete, then there is no computable embedding of Mod(T) into Mod(T′). Using this, we answer a question from [4], showing that there is no computable embedding of VS into ZS, where VS is the class of infinite vector spaces over Q, and ZS is the class of models of Th(Z, S). Similarly, (...) we show that there is no computable embedding of ACF into ZS, where ACF is the class of algebraically closed fields of characteristic 0. (shrink)

We extend results of Harizanov and Barker. For a relation R on a recursive structure /oA, we give conditions guaranteeing that the image of R in a recursive copy of /oA can be made to have arbitrary ∑α0 degree over Δα0. We give stronger conditions under which the image of R can be made ∑α0 degree as well. The degrees over Δα0 can be replaced by certain more general classes. We also generalize the Friedberg-Muchnik Theorem, giving conditions on a pair (...) of relations R and S under which the images of R and S can be made ∑α0 and independent over Δα0 in a recursive copy of /oA. (shrink)

Ash and Nerode [2] gave natural definability conditions under which a relation is intrinsically r. e. Here we generalize this to arbitrary levels in Ershov's hierarchy of Δmath image sets, giving conditions under which a relation is intrinsically α-r. e.

Let be a recursive structure, and let R be a recursive relation on . Harizanov isolated a syntactical condition which is necessary and sufficient for to have recursive copies in which the image of R is r.e. of arbitrary r.e. degree. We had conjectured that a certain extension of Harizanov's syntactical condition would be necessary and sufficient for to have recursive copies in which the image of R is ∑α0 of arbitrary ∑α0 degree, but this is not the case. Here (...) we give examples illustrating some restrictions on the possible ∑α0 degrees. In these examples, the image of R cannot be ∑α0 of degree d unless d possesses an “α-table”. (shrink)

We consider the following generalization of the notion of a structure recursive relative to a set X. A relational structure A is said to be a Γ-structure if for each relation symbol R, the interpretation of R in A is ∑math image relative to X, where β = Γ. We show that a certain, fairly obvious, description of classes ∑math image of recursive infinitary formulas has the property that if A is a Γ-structure and S is a further relation on (...) A, then the following are equivalent: For every isomorphism F from A to a Γ-structure, F is ∑math image relative to X, The relation is defined in A by a ∑math image formula with parameters. (shrink)

Only by misconstruing the term performative are the authors able to argue that males surpass females in “performative applications” of language. Linguistic performatives are not costly displays of quality, and syntax cannot be explained as an outcome of behavioural competition between pubertal males. However, there is room for a model in which language co-evolves with the unique human life-history stage of adolescence.

Previous studies have found that narrative input conveyed through different media influences the structure and content of children’s narrative retellings. Visual, televised narratives appear to elicit richer and more detailed narratives than traditional, orally transmitted storybook media. To extend this prior work and drawing from research on narrative elaboration, the current study’s main goal was to identify the core plot component differences (the who, what, where, when, why, and how of a story) between children’s retellings of televised versus traditional storybook (...) narratives. However, because children also differ individually in their IQ, we further incorporated this variable into our analysis of children’s narrative retellings. For our purpose, a novel coding schema was developed, following and extending the existing narrative elaboration approaches. Participants were 46 typically developing children aged 4–5 years from Germany. The current study incorporated two narrative input conditions to which children were randomly assigned: in the video condition, children watched a non-verbal, visually conveyed, televised story from a DVD; and in the book condition, children read the story with an adult and experienced an orally conveyed version in the form of a book with minimal accompanying pictures. In both conditions, the same story was conveyed. After including IQ as a covariate in our analyses, results show that the children from the video condition gave significantly more elaborated retellings, particularly across the who, what, and where (sub-)components. Differences between the conditions in the component when, how and why did not reach statistical significance. Our findings indicate that different media types entail differential cognitive processing demands of a story, resulting in type-specific memories and narratives. The effect of different medial conditions was significant and persisted when individual differences in cognitive development were considered. Consequences for children’s development, education, and interaction with and within today’s digital world are discussed. (shrink)

For a computable structure A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}}$$\end{document}, there may not be a computable infinitary Scott sentence. When there is a computable infinitary Scott sentence φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi}$$\end{document}, then the complexity of the index set I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I}$$\end{document} is bounded by that of φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi}$$\end{document}. There are results giving “optimal” Scott sentences for (...) structures of various familiar kinds. These results have been driven by the thesis that the complexity of the index set should match that of an optimal Scott sentence. In this note, it is shown that the thesis does not always hold. For a certain subgroup of Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Q}}$$\end{document}, there is no computable d-Σ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma_2}$$\end{document} Scott sentence, even though the index set is d-Σ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document}. (shrink)

For countable structure, "Scott rank" provides a measure of internal, model-theoretic complexity. For a computable structure, the Scott rank is at most [Formula: see text]. There are familiar examples of computable structures of various computable ranks, and there is an old example of rank [Formula: see text]. In the present paper, we show that there is a computable structure of Scott rank [Formula: see text]. We give two different constructions. The first starts with an arithmetical example due to Makkai, and (...) codes it into a computable structure. The second re-works Makkai's construction, incorporating an idea of Sacks. (shrink)

Nietzsche's opinions on philosophy and aesthetics developed under strong and lasting impulses from classical antiquity. These were not always the same, for at various periods in his life Nietzsche placed Heraclitus, Empedocles, Aeschylus, and even Socrates and Plato on the highest summit of wisdom. In his so-called first stage of development the pre-Socratics were generally his favourite thinkers, and in the third and last stage these same figures tend to come into prominence again. On the other hand, in the works (...) of Nietzsche's second, rationalistic period, when he was particularly influenced by Comte, Voltaire, and Darwin, Socrates and Plato—usually so hated and despised—are mentioned with affection, with gratitude or even with warm enthusiasm; and so, over and over again, is Epicurus. (shrink)

For about a hundred years there has been an intermittent but sometimes vigorous debate1 on the question whether Quintus Smyrnaeus and Tryphiodorus directly used the Second Aeneid as a source for their epic descriptions “of the capture and destruction of Troy. Heyne thought that they did not; but towards the end of the nineteenth century it appeared more likely that they did. Heinze opposed the general belief: but it was reaffirmed for Quintus by Paschal and Becker4 and for Tryphiodorus by (...) Dr. E. Cesareo on internal evidence. Meanwhile Professor Samuel E. Bassett had concluded that Quintus was not after all dependent on Vergil: and still more recently Dr. J. W. Mackail, reviewing Cesareo's monograph, has maintained with emphasis that the Aeneid is certainly not the source of the late epic. Accordingly the controversy cannot even now be considered closed. (shrink)

Increasingly, the role of health research in improving the discrepancies in health outcomes between Indigenous and non-Indigenous populations in developed countries is being recognised. Along with this comes the recognition that health research must be conducted in a manner that is culturally appropriate and ethically sound. Two key documents have been produced in Australia, known as The Road Map and The Guidelines, to provide theoretical and philosophical direction to the ethics of Indigenous health research. These documents identify research themes considered (...) critical to improving the health of the nation’s Indigenous peoples. They also provide values that, from an Indigenous perspective, are foundational to an ethical research process. This paper examines these research themes and values within the context of a current longitudinal birth cohort study of Indigenous infants and children in south-west Sydney: the Gudaga Study. Considerable time and effort have been invested in being true to the values stated in these documents: reciprocity; respect; equality; responsibility; survival and protection; and spirit and integrity. We have learnt that it is vital to be true to these values when conducting Indigenous health research—to quite literally “walk the talk”. (shrink)

The 2010 Nagoya Protocol is an international framework for access and benefit sharing (ABS) of the use of genetic and biological resources, with particular focus on indigenous communities. This is especially important in Africa, where local communities have a close reliance on environmental resources and ecosystems. However, national legislation and policies commonly lag behind international agreements, and this poses challenges for legal compliance as well as practical applications. This study reviews the academic literature on the Nagoya Protocol and ABS applications, (...) and then considers the implications of this analysis for research in Africa. Results show that there is uneven engagement with the principles of the Nagoya Protocol across different academic disciplines; local communities are sometimes sidelined in these studies; and only 8% of researchers in the literature analysed are located in Africa. Future developments should focus on ensuring national compliance with the Nagoya Protocol, and that researchers and industry work in partnership with local African communities on ABS issues. (shrink)