Shepherdson [14] showed that for a discrete ordered ring I, I is a model of IOpen iff I is an integer part of a real closed ordered field. In this paper, we consider integer parts satisfying PA. We show that if a real closed ordered field R has an integer part I that is a nonstandard model of PA (or even IΣ₄), then R must be recursively saturated. In particular, the real closure of I, RC (I), is recursively saturated. We (...) also show that if R is a countable recursively saturated real closed ordered field, then there is an integer part I such that R = RC(I) and I is a nonstandard model of PA. (shrink)

The ability to notice and reflect on distressing internal experiences from an objective perspective, often called psychological decentering, has been posited to be protective against mental health difficulties. However, little is known about how this skill relates to age across adolescence, its relationship with mental health, and how it may impact key domains such as affective executive control and social cognition. This study analysed a pre-existing dataset including mental health measures and cognitive tasks, administered to adolescents in Greater London and (...) Cambridge (mean age (SD) = 14.4 (1.77) years, N = 553). A self-report index of decentering based on available questionnaire items in the dataset was developed. Multiple linear regression was used to examine associations between decentering and mental health, affective executive control (measured using an affective Stroop Task, affective Working Memory Task, and affective Sustained Attention to Response Task) and social cognition. Higher decentering was significantly associated with lower depression and anxiety scores and higher psychological wellbeing. Results did not indicate significant relationships between decentering, affective executive control and social cognition. Further research is needed to discover cognitive mechanisms associated with this process, which could allow for optimisation of existing psychological therapy and reveal new avenues of intervention. (shrink)

Aggleton & Brown argue that a hippocampal-anterior thalamic system supports the “recollection” of contextual information about previous events, and that a separate perirhinal-medial dorsal thalamic system supports detection of stimulus “familiarity.” Although there is a growing body of human literature that is in agreement with these claims, when recollection and familiarity have been examined in amnesics using the process dissociation or the remember/know procedures, the results do not seem to provide consistent support. We reexamine these studies and describe the results (...) of an additional experiment using a receiver operating characteristic (ROC) technique. The results of the reanalysis and the ROC experiment are consistent with Aggleton & Brown's proposal. Patients with damage to both regions exhibit severe deficits in recollection and smaller, but consistent, deficits in familiarity. (shrink)

This essay considers P. J. Ivanhoe's critical challenge to Slingerland's analysis of wuwei(‘effortless action’). While I agree with Ivanhoe that we should do more work to embody and understand the concept of wuwei, I will defend Slingerland's notion that wuwei involves paradox—particularly in the cases of Zhuangi and Laozi. The present essay is not a defense of the specifics of Slingerland's analysis. Nonetheless, this essay focuses on defending the notion of paradox. Ivanhoe offers an alternative view of wuwei, one that (...) sees the paradox as a riddle. I argue that this kind of formulation would frame the problem of wuwei in an unhelpful manner. I offer several novel ways of overcoming, or at least qualifying, the experience of paradox that seems to be at play in nondoing. (shrink)

Burgess, J.P. and Rosen, G. Subject with No ObjectElliott, R.Faking Nature.

BackgroundJunior medical doctors have a key role in discussions and decisions about treatment and end-of-life care for people with dementia in hospital. Little is known about junior doctors’ decision-making processes when treating people with dementia who have advance care directives, or the factors that influence their decisions. To describe among junior doctors in relation to two hypothetical vignettes involving patients with dementia: their legal compliance and decision-making process related to treatment decisions; the factors influencing their clinical decision-making; and the factors (...) associated with accurate responses to one hypothetical vignette. MethodA cross-sectional survey of junior doctors, including trainees, interns, registrars and residents, on clinical rotation in five public hospitals located in one Australian state. The anonymous, investigator-developed survey was conducted between August 2018 and June 2019. Two hypothetical vignettes describing patients with dementia presenting to hospital with an ACD and either: bacterial pneumonia; or suspected stroke were presented in the survey. Participants were asked to indicate whether they would commence treatment, given the ACD instructions described in each vignette.ResultsOverall, 116 junior doctors responded. In Vignette 1, 58% of respondents selected the legally compliant option. Participants who chose the legally compliant option perceived ‘following patient wishes’ and ‘legal requirements to follow ACDs’ as equally important reasons for complying with the ACD. The most common reason for not selecting the legally compliant option in Vignette 1 was the ‘ACD is relevant in my decision-making process, but other factors are more relevant’. In Vignette 2, 72% of respondents indicated they would commence treatment and 18% selected they would not commence treatment.. Similar reasons influenced participant decision-making in Vignette 2, a less legally certain scenario.ConclusionsThere are critical gaps in junior doctors’ compliance with the law as it relates to the implementation of ACDs. Despite there being differences in relation to the legal answer and its certainty, clinical and ethical factors guided decision-making over and above the law in both vignettes. More education and training to guide junior doctors’ clinical decision-making and ensure compliance with the law is required. (shrink)

The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of "rank-homogeneous" trees. We consider these conditions as a possible definition of what it means for a class of structures to have "Ulm type". The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We apply (...) this result to show that there is no Turing computable embedding of the class of graphs into the class of "rank-homogeneous" trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a "rank-preserving" Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank ${\mathrm{\omega }}_{1}^{\mathrm{C}\mathrm{K}}$. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Pleasure of the PlayDeborah KnightThe Pleasure of the Play, by Bert O. States; 226 pp. Ithaca: Cornell University Press, 1994, $34.50, cloth, $12.95, paper.I am an Aristotelian about narrative structure. This is not always a fashionable position, and in some company I know just what to expect: a pop deconstructivist dressing down by those who assume that I must have simply missed the point of poststructuralism and (...) postmodernism. Surely, the nay-sayers claim, no one believes in beginnings, middles, and ends anymore—certainly not since Godard taught us that we don’t need to put them in that order. Isn’t it just obvious (they continue) that we must reject the ideology of wholeness and unity, and opt instead for fragmentation, or self-reflexivity, or other violations of Aristotelian form? And there is no mistaking that, in some quarters, notions like mimesis and catharsis haven’t received much good press lately.But there are still kindred Aristotelians, and Bert O. States is one. His The Pleasure of the Play takes the Poetics as its pivotal text and sets in motion around it a lively discussion of plays from, yes, Oedipus Rex to The Real Inspector Hound, stopping along the way to consider Shakespeare, Chekhov, Brecht, Handke (among others), before concluding with an essay on Samuel Beckett’s Catastrophe, a play dedicated to Václav Havel. States adopts an open rather than a closed view of what the Poetics has to say about tragedy, expanding the discussion well beyond tragedy itself, out toward drama and, indeed, comedy. But he is clearly unwilling to go as far as another group of Aristotelians, notably Paul Ricoeur, Alasdair MacIntyre, and Jerome Bruner, who treat narrative as a mode of actual lived existence. States’s objective is to show the continued vitality of the Poetics, especially in terms of what it can tell us about drama in cultural contexts much removed from the one which offered Aristotle his range of primary textual material. [End Page 272]To be clear, then, States doesn’t claim to be doing either Poetics “scholarship” or exegesis. Indeed, this book is not what one might typically think of as a philosophical examination of the Poetics. Anyone looking for such a thing would do well to consult the excellent but unmistakably philosophical Essays on Aristotle’s Poetics, edited by Amélie Oksenberg Rorty. States is doing something else here. Like Aristotle, he is showing how dramatic structures work.The book is engaging. It features wonderfully turned phrases, examples that immediately illuminate a point, and nicely interwoven references to a range of theorists and philosophers who only rarely are found in each other’s company, for example: Richard Boyd, Martin Heidegger, Douglas Hofstadter, Wolfgang Iser, Maurice Merleau-Ponty, Francis Sparshott, Tzvetan Todorov. Some of States’s more delightful examples might offend Aristotle purists. Hard cheese to them. Consider how States uses Roland Barthes’s analysis of the newspaper feature story, or fait divers, to illuminate the structure of the great dramatic plots. In States’s examples—GENERAL SACRIFICES DAUGHTER IN WEDDING CEREMONY (Iphigenia at Aulis) or WIFE FORCED INTO ADULTERY BY HUSBAND, MOTHER, PRIEST (Mandragola) or, to use Aristotle’s own example, MAN’S STATUE AVENGES HIS MURDER (pp. 67-68)—what each mock headline captures is the peculiar, often ironic, internal logic of drama. For States, this peculiar logic is characterized by events which are simultaneously improbable, unthinkable, unanticipatable, yet—given the unfolding course of actions—uncannily probable after all.Central to understanding this internal logic is the Aristotelian notion of peripety, the critical “divulging event” (p. 49) which turns out to be just the reverse of what one intended (as for example Oedipus killing his father and marrying his mother). Where Aristotle seems to treat peripety as a mere plot device, States considers it “a principle of plot development.” Thus, the status of peripety as a crucial dramatic plot device is “really a symptom” of its more basic function (p. 86). Peripety as a principle of plot development helps to show why it makes little sense to claim that what narratives imitate is “reality”—peripety is just what “open life” lacks (p... (shrink)

Readers expecting a history of nineteenth‐century pathology are in for a surprise. They will find instead a self‐conscious example of cultural studies, critical of some assumptions made in this field and of some feminist writing, but containing some alarming sentences like “My goal has been to give shape to the accidental palimpsests of an inveterately verbal, and increasingly visual, culture; to assemble a particular series of hermeneutic loose ends into a coherent account of how an extraordinarily bizarre system of signification (...) came into being” . With learned English like that, who needs Latin? But once we get into the main part of the book, things get much better. We are confronted with a study of the fringes of science, in popular writings, in literature, and in raree‐shows, one working from sources that the more austere scientifics of the Victorian period despised and that historians of science are prone to ignore. Metaphor and analogy are everywhere, and sensitive stomachs will be churned by vivid accounts of disease, deformity, and surgery.The first chapter is concerned with the cholera morbus, the plague of the nineteenth century, and with the way it could be perceived as an indicator of social ills. John Ruskin's word “illth” as an opposite of health is revived, and the terrible blackness of the shriveled and dehydrated victims of this disease imported from the East is linked with colonial and racist notions. The theme that a healthy body is like a well‐run state leads into the next chapter, on breast cancer. Surgery was not only agonizing but ineffective in the first half of the nineteenth century, but then the survival rate after three years rose gradually from 4.7 percent to 45 percent by 1900. O'Connor asks whether this saga, with cancer seen as cellular overproduction, reveals close connections with gender construction and the symbolic importance of breasts, concluding that it does not and that the language used really was neutral rather than sexual.She then looks at amputations and artificial limbs, seeing amputation as a threat to the whole masculine body that could be countered by prostheses almost undetectable to the observer. This allows reflection on illustration, where curiously disembodied hands are shown carrying out amputations; on dissembling and artificiality; on materialism; and on metaphors of wholeness and replacement and of extending senses and capacities. We see some extraordinary advertisements where men with artificial legs climb ladders and skate, perhaps on thin ice. The final chapter examines deformity, with monsters and freaks . P. T. Barnum is prominent here, but interesting links are also made to the Great Exhibition at the Crystal Palace and its successors and the numerous museums that were such a feature of the Victorian period. They are strikingly placed in a continuum, rather than opposed, in a discussion of chaos and order, capitalism and health, deformity and degeneration. Wonder is presented as the key to modern sensibility, and there is a nice quotation on page 152: “If Beauty and the Beast should be brought into competition in London at the present day, Beauty would stand no chance against the Beast in the race for popularity.” Readers will have been led into a fascinating world at the periphery of the respectable science that most of us study and will rejoice in the extraordinary sights they see. (shrink)

We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.

An application of the Method of Analysis of Relational Complexity (MARC) to suppositional reasoning in the knight-knave task is outlined. The task requires testing suppositions derived from statements made by individuals who either always tell the truth or always lie. Relational complexity (RC) is defined as the number of unique entities that need to be processed in parallel to arrive at a solution. A selection of five ternary and five quaternary items were presented to 53 psychology students using a (...) pencil and paper format. A computer-administered version was presented to 50 students. As predicted, quaternary problems were associated with higher error rates and longer response times than ternary problems. The computer-administered form was more difficult than the pencil and paper version of the test. These differences are discussed in terms of RC theory and alternative processing accounts. Together, they indicate that the relational complexity metric is a useful and parsimonious way to quantify complexity of reasoning tasks. (shrink)

THE HOLY GAL - and European, medieval legends - a mysterious vessel, for the sake of approaching and engaging in its good deeds, the knights performed their exploits. It was commonly believed that this is the Cup with the blood of Jesus Christ, which Joseph of Arimathea gathered, who removed from the cross the body of the crucified Christ. It was often assumed that this cup originally served Christ and the Apostles at the time of the Last Supper; was the (...) Cup for the communion of the first Liturgy. Gral is a mystery, invisible to the unworthy, but also worthy of being different. Gral has the ability to miraculously fill his elect with unearthly things, which was first discovered during the imprisonment of Joseph Artmofeysky. (shrink)

An introduction to philosophy through film, _Thinking Through Film: Doing Philosophy, Watching Movies_ combines the exploration of fundamental philosophical issues with the experience of viewing films, and provides an engaging reading experience for undergraduate students, philosophy enthusiasts and film buffs alike. An in-depth yet accessible introduction to the philosophical issues raised by films, film spectatorship and film-making Provides 12 self-contained, close discussions of individual films from across genres Films discussed include Total Recall, Minority Report, La Promesse, Funny Games, Ikuru, The (...) Dark Knight, Memento, AI and more Explores concepts that span epistemology, metaphysics, fate, choice, robot love, time travel, personal identity, spectacle, ethics, luck, regret, consequentialism, deontology and the philosophy of film itself A uniquely flexible resource for courses in philosophy and film that encourages student reflection, as well as being an engaging read for the film enthusiast. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Intertextual Biography in the Rivalry of Cratinus and AristophanesZachary P. BilesMore than a decade ago, Malcolm Heath provided an influential explanation for charges of plagiarism between comic poets when he posited a growing store of ideas that were recycled as quickly as they were invented. As a result, "Anything put on stage in a comedy would become public property and be absorbed into the repertoire, so that all comic (...) poets contributed to it; and all drew on it, although each would aim to give a new and original twist to the material which he borrowed, so that the repertoire constantly evolved. If this was so, then any poet could lay claim to originality... and any rival could make a counterclaim of plagiarism."1 These remarks have important implications for the study of Old Comedy, not least in exposing the irony of such assertions as that of Antiphanes (Poiēsis, fr. 189 K-A), which overstates generic distinctions between tragedy and comedy on the score of originality. Beyond merely acknowledging comedy's essentially adaptive nature, Heath's position suggests that a certain degree of allusiveness was, as it were, built into the genre. Unfortunately there are few opportunities to test the potential insights that follow from Heath's general proposition since the corpus of comic fragments poses so many questions of plot, context, attribution, and-always important for this kind of study-chronology.There is one sequence of plays, however, that has attracted attention since antiquity as an example of comic poets responding to one another and for which valuable insights can still be gained by building on Heath's thesis. In 423 Cratinus took the prize against Aristophanes' Clouds with Pytine, a play in which Cratinus boldly portrayed himself as the hero while borrowing heavily from Aristophanes' caricature of him in Knights the previous year. While interest in the relationship of these plays has been renewed in recent years, the convergence of issues pertaining to adaptation, intertextuality, and rivalry has not been fully explored. Besides discussing these ideas as they relate to Knights and [End Page 169] Pytine, I shall extend the thread of artistic borrowing at either end, first by positing a stage autobiography of Cratinus that both predates and inspired Knights, and then by tracing elements of intertextuality between Wasps and Pytine. Generally speaking Heath's model proves to be of great value; however, my study makes an important modification by treating competition as a vital aspect of comic poetry.2 The intertextuality of these plays primarily depends on poetic biography, and the notion of competition is central to my understanding of stage biography as comic poets employed it either to assert their own superiority or malign their rivals. After examining the biographical interplay in the rivalry of Cratinus and Aristophanes, I end by applying the intertextual model more generally to Wasps, a play that advertises itself as a competitive response and whose intertextual relationship with Pytine can be viewed as a function of competitive strategy.IThe trail of evidence begins with a scholion on Knights 400. Commenting on the chorus's elusive response to Cleon ("If I don't despise you, may I become a blanket in Cratinus' house!"), the scholiast writes:(= Pytine test. ii K-A)3 [End Page 170]Certain errors about Cratinus' retirement aside,4 the scholiast shows himself to be a reliable witness to the play by his knowledge of the plot and ability to cite the text in the continuation of his commentary (fr. 193). Thus, with the exception of treating the more fully developed caricature of Cratinus as a drunk in the Knights parabasis as the actual source of inspiration for his self-portrayal in Pytine, generations of scholars have followed the scholiast's characterization of Pytine as a redemptive play, however exaggerated this biographical (mis)representation may have been in both plays. Two recent studies have raised objections to the traditional understanding of Knights and Pytine. Troubled by a certain feeling of allusiveness in the jokes about Cratinus in Knights and Acharnians, Keith Sidwell hypothesizes a source for the audience's familiarity with details of Cratinus' life by arguing that his stage "biography " was not an Aristophanic... (shrink)

“More than any other living scholar of medieval philosophy, Gyula Klima has influenced the way we read and understand philosophical texts by showing how the questions they ask can be placed in a modern context without loss or distortion. The key to his approach is a respect for medieval authors coupled with a commitment to regarding their texts as a genuine source of insight on questions in metaphysics, theology, psychology, logic, and the philosophy of language—as opposed to assimilating what they (...) say to modern doctrines, or using medieval discussions as a foil for ‘new and improved’ conceptual schemes.” Jack Zupko, University of Alberta “Gyula Klima is widely recognized as one of the world’s leading experts on thirteenth and fourteenth-century Latin philosophy, with his own, distinctive analytic approach, which brings out both the similarities and differences between medieval and contemporary logic and semantics.” John Marenbon, Trinity College, University of Cambridge “Gyula Klima has been a towering figure in the field of medieval philosophy for decades. His influence comprises not only the scholarly results of his work, but also intense and generous mentorship of students and junior colleagues. This volume is a perfect reflection of the esteem that he enjoys around the world, collecting excellent pieces by established as well as up-and-coming scholars of medieval philosophy.” Catarina Dutilh Novaes, Vrije Universiteit Amsterdam “For four decades now, Gyula Klima has been setting the standard among medievalists for philosophical sophistication and historical rigor. This collection of wide-ranging studies from leading scholars in the field offers a worthy tribute to that legacy.” Robert Pasnau, University of Colorado Boulder Gyula Klima is Professor of Philosophy at Fordham University, and Senior Research Fellow, Consultant, and the Director of Institute for the History of Ideas of the Hungarian Research Institute in Budapest. In 2022, the President of Hungary awarded him the Knight’s Cross of the Hungarian Order of Merit, “in recognition of his outstanding academic career, significant research work and exemplary leadership.” In this volume, colleagues, collaborators, and students celebrate Klima’s project with new essays on Plotinus, Anselm, Aquinas, Buridan, Ockham and others, exploring specific questions in philosophy of mind, philosophy of language, metaphysics, and logic. No contemporary surpasses Kripke and Klima in semantics and metaphysics, but only Gyula Klima’s thought ranges flawlessly over classical philosophy as well. The volume is a fitting tribute to the master. David Twetten, Marquette University. (shrink)

I Assume that in Latin there was a stress accent which, in the time of Lucretius, was governed by the well-known ‘law of the penultimate’; also that in Latin poetry, although the metre is determined by the quantity of the syllable, nevertheless the stress accent must not be ignored. In fact, the inter-relation of the ictus of the quantitative metre with the stress accent is a most important factor in determining the rhythm of the verse. It is well known that (...) in the Latin hexameter special importance was attached to the coincidence of ictus and accent in the fifth and sixth feet, so as to secure a characteristic and definite ending to the line. But the coincidence or clash of ictus and accent has its effect in every foot, although to a less extent. Particularly in the fourth foot is it important. There is an obvious difference between a line in which stress accent reinforces the ictus in the fourth, fifth, and sixth feet, and a line in which conflict occurs between ictus and accent in the fourth foot. W. F. J . Knight refers to these lines as homodyned and heterodyned. Each foot of the hexameter could be examined for the effect of homodyne and heterodyne; I am limiting this discussion to the fourth foot. In classifying fourth feet as homodyned or heterodyned, I have described as homodyned a foot in which a stress accent coincides with the ictus; all other feet are heterodyned. It must be realized, however, that there are possible varieties of homodyned fourth feet. They may be spondaic or dactylic; they may be caused by the overlap of the last two syllables of a polysyllabic word, or they may consist of a single word or two words. There is a great difference of metrical effect. Heterodyned lines may again be differentiated between those which contain a stress accent clashing with the ictus, and those in which there is no stress accent at all. (shrink)

Knight has shown how the moral growth of medical students involves a spiritual journey. He may, however, present too sanguine a portrayal of the extent to which the medical education environment promotes this moral and spiritual growth. Medical school may indeed be more abusive than supportive. Admitting more women to medical school and teaching more humanities courses, while worthwhile, will not necessarily promote the goals that Knight appropriately advocates.

This essay introduces a special report from The Hastings Center entitled Democracy in Crisis: Civic Learning and the Reconstruction of Common Purpose, which grew out of a project supported by the John S. and James L. Knight Foundation. This multiauthored report offers wide‐ranging assessments of increasing polarization and partisanship in American government and politics, and it proposes constructive responses to this in the provision of objective information, institutional reforms in government and the electoral system, and a reexamination of cultural (...) and political values needed if democracy is to function well in a pluralistic and diverse society. The essays in the special report explore the norms of civic learning and institutions, social movements, and communal innovations that can revitalize civic learning in practice. This introductory essay defines and explains the notion of civic learning, which is a lynchpin connecting many of the essays in the report. Civic learning pertains to the ways in which citizens learn about collective social problems and make decisions about them that reflect the duties and responsibilities of citizenship. Such learning can occur in many social settings in everyday life, and it can also be facilitated through participation in the processes of democratic governance on many levels. Civic learning is not doctrinaire and is compatible with a range of public goals and policies. It is an activity that increases what might be called the democratic capability of a people. (shrink)

The little we know with certainty about Eupolis' Marikas can be summarised in a few lines. The play was produced at the Lenaea of 421 b.c. The demagogue Hyperbolus was satirised under the name of Marikas, and was represented as a man of little or no culture . Marikas/Hyperbolus was a slave. This has been denied in the past, but is now made clear by the commentary on the Marikas in P. Oxy. 2741 πρς [ν] δεσπότην Ὑπέρβολος. Aristophanes complained in (...) the Clouds we possess that Eupolis had availed himself of the Knights for his Marikas , and it is in fact possible that the idea of Marikas as a slave was borrowed from the Knights, because some of his traits seem to correspond to those of the Aristophanic Sausage-seller. The play apparently had two semi-choruses, one of rich and one of poor people. The point of the name Marikas has long been debated. Ancient sources are at least agreed that it is ‘barbarian’. Herodianus 1.50,12 Lentz does not go beyond stating that Marikas is an νομα βάρβαρον παρ τ κωμικ . Hesych. μ 283 Latte has more to offer: Μαρικν· κίναιδον. ο δ ποκόρισμα παιδίου ρρενος βαρβαρικόν. (shrink)

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out a sequence of examples. We follow recent work by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. (...) In this paper, we calculate the degree of the isomorphism problem for Abelian p-groups of bounded Ulm length. The result is a sequence of classes whose isomorphism problems are cofinal in the hyperarithmetical hierarchy. In the process, new back-and-forth relations on such groups are calculated. (shrink)

In 2004 Csima, Hirschfeldt, Knight, and Soare [1] showed that a set A ≤T 0' is nonlow₂ if and only if A is prime bounding, i.e., for every complete atomic decidable theory T, there is a prime model M computable in A. The authors presented nine seemingly unrelated predicates of a set A, and showed that they are equivalent $\Delta _{2}^{0}$ sets. Some of these predicates, such as prime bounding, and others involving equivalence structures and abelian p-groups come from (...) model theory, while others involving meeting dense sets in trees and escaping a given function come from pure computability theory. As predicates of A, the original nine properties are equivalent for $\Delta _{2}^{0}$ sets; however, they are not equivalent in general. This articale examines the (degree-theoretic) relationship between the nine properties. We show that the nine properties fall into three classes, each of which consists of several equivalent properties. We also investigate the relationship between the three classes, by determining whether or not any of the predicates in one class implies a predicate in another class. (shrink)