Primary progressive aphasia is a clinical syndrome in which patients progressively lose speech and language abilities. Three variants are recognized: logopenic, associated with phonology and/or short-term verbal memory deficits accompanied by left temporo-parietal atrophy; semantic, associated with semantic deficits and anterior temporal lobe atrophy; non-fluent associated with grammar and/or speech-motor deficits and inferior frontal gyrus atrophy. Here, we set out to investigate whether the three variants of PPA can be dissociated based on error patterns in a single language task. We (...) recruited 21 lvPPA, 28 svPPA, and 24 nfvPPA patients, together with 31 healthy controls, and analyzed their performance on an auditory noun-to-verb generation task, which requires auditory analysis of the input, access to and selection of relevant lexical and semantic knowledge, as well as preparation and execution of speech. Task accuracy differed across the three variants and controls, with lvPPA and nfvPPA having the lowest and highest accuracy, respectively. Critically, machine learning analysis of the different error types yielded above-chance classification of patients into their corresponding group. An analysis of the error types revealed clear variant-specific effects: lvPPA patients produced the highest percentage of “not-a-verb” responses and the highest number of semantically related nouns ; in contrast, svPPA patients produced the highest percentage of “unrelated verb” responses and the highest number of light verbs. Taken together, our findings indicate that error patterns in an auditory verb generation task are associated with the breakdown of different neurocognitive mechanisms across PPA variants. Specifically, they corroborate the link between temporo-parietal regions with lexical processing, as well as ATL with semantic processes. These findings illustrate how the analysis of pattern of responses can help PPA phenotyping and heighten diagnostic sensitivity, while providing insights on the neural correlates of different components of language. (shrink)

This vibrant collection of papers by an interdisciplinary group of authors -- psychologists, theologians, and social scientists -- presents brilliant new perspectives on spirituality, ethics, and relationship. In their diversity of views, their Intellectual and spiritual dynamism, the authors bring power and hope to this subject so central to the human experience.

In lieu of an abstract, here is a brief excerpt of the content:Citizenship and Culture in Early Modern EuropePeter N. MillerCharlotte Wells, Law and Citizenship in Early Modern France (Baltimore: The Johns Hopkins University Press, 1995), xviii, 198p.Paula Findlen, Possessing Nature: Museums, Collecting, and Scientific Culture in Early Modern Italy (Berkeley, Los Angeles, and London: University of California Press, 1994), xviii, 449p.Steven Shapin, The Social History of Truth: Civility and Science in Seventeenth-Century England (Chicago and London: University of Chicago Press, (...) 1994), xxiv, 483p.Anne Goldgar, Impolite Learning: Conduct and Community in the Republic of Letters 1680–1775 (New Haven and London: Yale University Press, 1995), xv, 395p.Lawrence Klein, Shaftesbury and the Culture of Politeness: Moral Discourse and Cultural Politics in Early Eighteenth-Century England (Cambridge, U.K., 1994), xiii, 217p.Daniel Gordon, Citizens Without Sovereignty: Equality and Sociability in French Thought, 1670–1789 (Princeton: Princeton University Press, 1994), viii, 270p.Dena Goodman, The Republic of Letters: A Cultural History of the French Enlightenment (Ithaca and London: Cornell University Press, 1994), xiii, 338p.E. J. Hundert, The Enlightenment’s “Fable”: Bernard Mandeville and the Discovery of Society (Cambridge: Cambridge University Press, 1994), xii, 284p.The pre-modern political world was broken and remade in the two centuries that separate Montaigne from Jefferson. The long agony of the mixed constitution that began in the civil wars which raged in Iberia, France, the Low Countries, and England and seemed settled by the widespread adoption of the maxims of reason of state, revived at the end of the period, with revolution in Poland, Denmark, Sweden, Geneva, and, more famously, [End Page 725] British North America and France. The problem, classically, turned on the location of sovereignty, or supreme authority, in political systems designed to balance and diffuse rather than concentrate power. When budget deficits and fratricidal culture wars raised the cry of “necessity”—with the knowledge, of course, that necessity knew no law—estates and kings across Europe found themselves at daggers drawn. The claim that the ruler, who naturally was wholly committed to the common good, had therefore the ability to take emergency action was used both by those accustomed to rule and those newly attained to it by force. The pursuit of an “interest” that was identified with the nation’s effectively marginalized discussions of right and law while still serving an essentially constitutional, justificatory role in political debate. But if unchecked authority was necessary in order to meet the challenge of a world characterized by change and chance and thus had to reside somewhere, was there anything that made its exercise by one body more appropriate than another? This was the question that lay behind the late eighteenth-century repudiation of the reason of state “solution” to the problem of the mixed constitution. The answer, which clearly underpinned the establishment in fact of what had first been theorized already a century earlier, was that only consent could legitimate the exercise of sovereignty in time of necessity.1Representation, in one form or another, was the acknowledged solution to the problem formulated by Hobbes: “the name of Tyranny, signifieth nothing more, nor less, than the name of Sovereignty, be it in one, or many men, saving that they that use the former word are understood to be angry with them they call Tyrants.” But representation also acknowledged the reality behind the charged category of “citizenship”: most people in most places could not be said to live the life of the active citizen celebrated in Roman republican literature. Hence Hobbes’s attack on recourse to classical exempla in general, and the Libertas of Lucca in particular. The idea of civis as law-abiding subject was as radical a redrawing of the terms of debate as the identification of human nature with unsociability. Insofar as politics, classically, justified itself as the means for individual self-perfection, the practice of the ancient citizen could be conceived of as the practice of that best life speculated upon by philosophers. For the represented citizen, however, politics necessarily occupied a more subsidiary position. What, then, defined the best life to which he could aspire?There is no simple answer to this question, and the early modern ambivalence has persisted into our own time... (shrink)

BackgroundIn the Canadian Alliance for Healthy Hearts and Minds (CAHHM) cohort, participants underwent magnetic resonance imaging (MRI) of the brain, heart, and abdomen, that generated incidental findings (IFs). The approach to managing these unexpected results remain a complex issue. Our objectives were to describe the CAHHM policy for the management of IFs, to understand the impact of disclosing IFs to healthy research participants, and to reflect on the ethical obligations of researchers in future MRI studies.MethodsBetween 2013 and 2019, 8252 participants (...) (mean age 58 ± 9 years, 54% women) were recruited with a follow-up questionnaire administered to 909 participants (40% response rate) at 1-year. The CAHHM policy followed a restricted approach, whereby routine feedback on IFs was not provided. Only IFs of severe structural abnormalities were reported.ResultsSevere structural abnormalities occurred in 8.3% (95% confidence interval 7.7–8.9%) of participants, with the highest proportions found in the brain (4.2%) and abdomen (3.1%). The majority of participants (97%) informed of an IF reported no change in quality of life, with 3% of participants reporting that the knowledge of an IF negatively impacted their quality of life. Furthermore, 50% reported increased stress in learning about an IF, and in 95%, the discovery of an IF did not adversely impact his/her life insurance policy. Most participants (90%) would enrol in the study again and perceived the MRI scan to be beneficial, regardless of whether they were informed of IFs. While the implications of a restricted approach to IF management was perceived to be mostly positive, a degree of diagnostic misconception was present amongst participants, indicating the importance of a more thorough consent process to support participant autonomy.ConclusionThe management of IFs from research MRI scans remain a challenging issue, as participants may experience stress and a reduced quality of life when IFs are disclosed. The restricted approach to IF management in CAHHM demonstrated a fair fulfillment of the overarching ethical principles of respect for autonomy, concern for wellbeing, and justice. The approach outlined in the CAHHM policy may serve as a framework for future research studies.Clinical trial registrationhttps://clinicaltrials.gov/ct2/show/nct02220582. (shrink)

This report describes the rationale, approaches, organization, and resource development leading to a large-scale deletion bin map of the hexaploid wheat genome. Accompanying reports in this issue detail results from chromosome bin-mapping of expressed sequence tags representing genes onto the seven homoeologous chromosome groups and a global analysis of the entire mapped wheat EST data set. Among the resources developed were the first extensive public wheat EST collection. Described are protocols for sequencing, sequence processing, EST nomenclature, and the assembly of (...) ESTs into contigs. These contigs plus singletons were used for selection of distinct sequence motif unigenes. Selected ESTs were rearrayed, validated by 5′ and 3′ sequencing, and amplified for probing a series of wheat aneuploid and deletion stocks. Images and data for all Southern hybridizations were deposited in databases and were used by the coordinators for each of the seven homoeologous chromosome groups to validate the mapping results. Results from this project have established the foundation for future developments in wheat genomics. (shrink)

We examine the sequences A that are low for dimension, i.e. those for which the effective dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness. By considering analogues of characterizations of lowness for randomness, we show that lowness for dimension can be characterized in several ways. It is equivalent to lowishness for randomness, namely, that every Martin-Löf random sequence has effective dimension (...) 1 relative to A, and lowishness for K, namely, that the limit of KA/K is 1. We show that there is a perfect [Formula: see text]-class of low for dimension sequences. Since there are only countably many low for random sequences, many more sequences are low for dimension. Finally, we prove that every low for dimension is jump-traceable in order nε, for any ε > 0. (shrink)

We prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the maximal (...) value of ${\rm{\hat{\Omega }}}$ must be random, the minimal value must be Turing complete, and that ${\rm{\hat{\Omega }}}\left \oplus X{ \ge _T}\emptyset \prime$ for every X. We also obtain some machine-dependent results, including that for every $\varepsilon > 0$, there is a universal machine V such that ${{\rm{\hat{\Omega }}}_V}$ maps every real X having effective Hausdorff dimension greater than ε to a real of effective Hausdorff dimension 0 with the property that $X{ \le _{tt}}{{\rm{\hat{\Omega }}}_V}\left$; and that there is a real X and a universal machine V such that ${{\rm{\Omega }}_V}\left$ is rational. (shrink)

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy of (...) subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory.We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each n. (...) A tower is maximal if there is no infinite computable set contained in all $G_n$. A tower ${\left \langle {G_n}\right \rangle }_{n\in \omega }$ is an ultrafilter base if for each computable R, there is n such that $G_n \subseteq ^* R$ or $G_n \subseteq ^* \overline R$ ; this property implies maximality of the tower. A sequence $(G_n)_{n \in {\mathbb N}}$ of sets can be encoded as the “columns” of a set $G\subseteq \mathbb N$. Our analogs of ${\mathfrak t}$ and ${\mathfrak u}$ are the mass problems of sets encoding maximal towers, and of sets encoding towers that are ultrafilter bases, respectively. The relative position of a cardinal characteristic broadly corresponds to the relative computational complexity of the mass problem. We use Medvedev reducibility to formalize relative computational complexity, and thus to compare such mass problems to known ones.We show that the mass problem of ultrafilter bases is equivalent to the mass problem of computing a function that dominates all computable functions, and hence, by Martin’s characterization, it captures highness. On the other hand, the mass problem for maximal towers is below the mass problem of computing a non-low set. We also show that some, but not all, noncomputable low sets compute maximal towers: Every noncomputable (low) c.e. set computes a maximal tower but no 1-generic $\Delta ^0_2$ -set does so.We finally consider the mass problems of maximal almost disjoint, and of maximal independent families. We show that they are Medvedev equivalent to maximal towers, and to ultrafilter bases, respectively. (shrink)

We say that E is R-sparse if f(Ek) has no interior, for each k 2 N and f : Rk ! R de nable in R. (Throughout, \de nable" means \de nable without parameters".) In this note, we consider the extent to which basic metric and topological properties of subsets of R de nable in (R;E)# are determined by the corresponding properties of subsets of R de nable in (R;E), when R is an o-minimal expansion of (R;<;+;0;1) and E is (...) R-sparse. The precise statement of the main result is a bit complicated, but we can state some special cases now. (shrink)

This article explores the possible interpretations—and the implications of those interpretations—of a comment about the importance of art made by Yasunari Kawabata (1899–1972), later the first Japanese Nobel laureate for literature: that “looking at old works of art is a matter of life and death.” (In 1949, Kawabata visited Hiroshima in his capacity as president of the Japan literary society P.E.N. to inspect the damage caused by the atomic bombing of Hiroshima that helped end World War II. On his way (...) back to his home in Kamakura, he stopped in Kyoto. He came under severe criticism for “sightseeing” at such a time. This comment was his response.) The introduction explains why we should take him seriously as a commentator on art. The body of the article examines why our looking at art might be more, not less, important after the post-War situation, the kinds of art Kawabata might have meant, why some possibilities are more likely than others, and how they differ in what they offer us and the value of art under conditions of trauma and mass trauma. (shrink)

Defining the degree of categoricity of a computable structure ${\mathcal{M}}$ to be the least degree d for which ${\mathcal{M}}$ is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above 0 (n) can be so realized, as can the degree 0 (ω).

An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first (...) main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n−g. Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic.Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree.Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α<1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. (shrink)

Importance Informed consent is essential to ethical, rigorous research and is important to recruitment and retention in cancer trials.Objective To examine cancer clinical trial (CCT) participants’ perceptions of informed consent processes and variations in perceptions by cancer type.Design and Setting and Participants Cross-sectional survey from mixed-methods study at National Cancer Institute–designated Northeast comprehensive cancer center. Open-ended and forced-choice items addressed: (1) enrollment and informed consent experiences and (2) decision-making processes, including risk-benefit assessment. Eligibility: CCT participant with gastro-intestinal or genitourinary, hematologic-lymphatic (...) malignancies, lung cancer, and breast or gynecological cancer (N = 334).Main Outcome Measures Percentages satisfied with consent process and information provided; and assessing participation’s perceptions of risks/benefits. Multivariable logistic or ordinal regression examined differences by cancer type.Results Most patient-participants felt well informed by the consent process (more than 90% overall and by cancer type) and. most (87.4%) reported that the consent form provided all the information they wanted, although nearly half (44.8%) reported that they read the form somewhat carefully or less. More than half (57.9%) said that talking to research staff (i.e., the consent process) had a greater impact on participation decisions than reading the consent form (2.1%). A third (31.1%) were very sure of joining in research studies before the informed consent process (almost half of lung cancer patients did—47.1%). Most patients personally assessed the risks and benefits before consenting. However, trust in physicians played an important role in the decision to enroll in CCT.Conclusions and Relevance Cancer patients rely less on written features of the informed consent process than on information obtained from the research staff and their own physicians. Research should focus on information and communication strategies that support informed consent from referring physicians, researchers, and others to improve patient risk-benefit assessment and decision-making. (shrink)

What is the temporal course of gratitude and indebtedness and how do these feelings influence helping in the context of reciprocity? In an online-game tapping real-life behaviour, Study 1 (N = 106) finds that while gratitude towards a benefactor remains elevated after an opportunity to reciprocate, indebtedness declines along with helping. Yet, indebtedness rather than gratitude better predicts real-life helping of a benefactor. Using a vignette-based experiment, Study 2 (N = 217) finds that after reciprocation indebtedness and likelihood of helping (...) a benefactor reset to a baseline level while gratitude endures. Furthermore, the decrease in helping after reciprocation is better explained by indebtedness than by gratitude. Study 3 (N = 217) assessed the unique influences of gratitude and indebtedness on helping by comparing contexts in which gratitude is at a baseline level but indebtedness is elevated (e.g. before a monetary payment for a service received) to contexts in which indebtedness is at a baseline level but gratitude is elevated (e.g. after reciprocation of benefits freely given by a friend). People are more likely to help in the former compared to latter context, and this difference is better explained by indebtedness rather than by gratitude. We discuss the interrelated and understudied relationships between gratitude, indebtedness, and reciprocity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 249 Girolamo Balduino: Ricerche sulla logica della Scuola di Padova nel Rinascimento. By Giovanni Papuli. (Bark Lacerta, Universith di Bari, Pubblicazioni dell'lstituto di filosofia, 12, 1967. Pp. 313. no price.) The philosophers at the University of Padua during the late Middle Ages and Renaissance arc attracting much renewed interest. This study makes accessible again the logical philosophy of Girolamo Balduino, professor at Padua during the second quarter (...) of the sixteenth century. Like other thinkers of his period, 13alduino follows the logic of Aristotle, and looks for progress within the ancient and mediaeval tradition, not for radically new doctrines. He continues the traditional interpretation of Aristotle by Averroes, for whom logic is only an instrumental habitus, a tool or method of demonstration. About the final contribution of the school of Padua to the improvement of Aristotelian logic was the doctrine of regressive demonstration, where demonstration terminates in or discloses the definition. Zabarella's well-known teaching on this point seems to be derived entirely from Balduino. Contrary to the interpretation of Cassirer, followed by Randall, this regressive demonstration is not a universal method of inquiry and is not at all like, and not the historical source of, the new method of Galileo. Papuli's book is solidly based on the original Latin texts, in notes, which are of great value in view of the fact that Balduino's works have been out of print since 1573. Not all of Papuli's interpretations are beyond criticism (e.g., p. 296), but he has done a service in enabling us to reestablish contact with one of the last significant commentators on Aristotle's logic. PAUL J. W. MILLER University of Colorado Documents sur la vie de Jules-Cdsar Vanini de Taurisano. By Emile Namer. (Bari: Adriatica Editrice, n.d.=Univcrsith degli Studi di Bari, Pubblicazioni delFIstituto di Filosofia, II serie, Testi e Documenti, I. Pp. 196+22 facsimile illustrations) Giulio Cesare Vanini (1585-1619) ranks with Giordano Bruno as a modern hero of freedom of philosophical expression. He was tortured and then burned at the stake in Toulouse at the age of thirty-four, because of the unorthodoxy of his views. For this reason, he has drawn more attention than is perhaps deserved on the basis of his rather mediocre writings, which are little more than a tissue of plagiarisms culled from Pomponazzi, Cardano, J. C. Scaliger, and others. In this volume, Emile Namer has collected the scattered documents dealing with Vanini's life and activities. This is a valuable service, for it should enable scholars to disentangle fact from fiction and reality from myth. There has been so much heated discussion regarding Vanini that it is now time that someone should attempt to establish the precise facts and to reevaluate Vanini's place in intellectual history. In the past, writings about him have been governed more often by emotion than by reason. Namer prints documents from Naples, London, Paris, Simancas, and Toulouse. Some of these have been printed before in various journal articles, but it is valuable to have them all together in a single volume. In addition, he prints relevant excerpts concerning--as one of them put it--le douzi~me apostre de Satan, including material from Mersenne, Garasse, and others. He also includes a series of facsimiles of sample pages from the documents which he prints. All in all Namer's work is competently 250 HISTORY OF PHILOSOPHY done, though perhaps a bit more annotation to put the documents in historical perspective would have been desirable. In any case this little volume must be one of the bases for any future serious biographical or interpretative studies dealing with Vanini. Moreover, it shouM also be useful for scholars dealing with more general questions of seventeenth-century intellectual, religious, and social history. Unfortunately, there is no index, nor bibliography of earlier literature on Vanini, and the Introduction is perhaps too brief to orient the reader who has little previous knowledge of Vanini. CHARLES B. SCHMITT University oJ Leeds Tommaso Campanella: Renaissance Pioneer o[ Modern Thought. By Bernardino M. Bonansea. (Washington: Catholic University of America Press, 1969. Pp. xi 421. $14.50) This excellent critical study of the life and... (shrink)

We show that if add(null) = c, then the globally Baire and universally measurable chromatic numbers of the graph of any Borel function on a Polish space are equal and at most three. In particular, this holds for the graph of the unilateral shift on [N]N, although its Borel chromatic number is N₀. We also show that if add(null) = c, then the universally measurable chromatic number of every treeing of a measure amenable equivalence relation is at most three. In (...) particular, this holds for "the" minimum analytic graph G₀ with uncountable Borel (and Baire measurable) chromatic number. In contrast, we show that for all κ ∈ {2, 3...., N₀. c}, there is a treeing of E₀ with Borel and Baire measurable chromatic number κ. Finally, we use a Glimm—Effros style dichotomy theorem to show that every basis for a non-empty initial segment of the class of graphs of Borel functions of Borel chromatic number at least three contains a copy of (R<N, ⊇). (shrink)

In this paper we will consider two possible definitions of projective subsets of a separable metric space X. A set A subset of or equal to X is Σ11 iff there exists a complete separable metric space Y and Borel set B subset of or equal to X × Y such that A = {x ε X : there existsy ε Y ε B}. Except for the fact that X may not be completely metrizable, this is the classical definition of (...) analytic set and hence has many equivalent definitions, for example, A is Σ11 iff A is relatively analytic in X, i.e., A is the restriction to X of an analytic set in the completion of X. Another definition of projective we denote by ΣX1 or abstract projective subset of X. A set of A subset of or equal to X is ΣX1 iff there exists an n ε ω and a Borel set B subset of or equal to X × Xn such that A = {x ε X:there existsy ε Xn ε B}. These sets ca n be far more pathological. While the family of sets Σ11 is closed under countable intersections and countable unions, there is a consistent example of a separable metric space X where ΣX1 is not closed under countable intersections or countable unions. This takes place in the Cohen real model. Assuming CH, there exists a separable metric space X such that every Σ11 set is Borel in X but there exists a Σ11 set which is not Borel in X2. The space X2 has Borel subsets of arbitrarily large rank while X has bounded Borel rank. This space is a Luzin set and the technique used here is Steel forcing with tagged trees. We give examples of spaces X illustrating the relationship between Σ11 and ΣX1 and give some consistent examples partially answering an abstract projective hierarchy problem of Ulam. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Notes and Discussions PARMENIDES THE PROPHET~ The latest word on Parmenides comes from a recent and exhaustive study by Leonardo Tar~n. 1 Among other illuminating and novel interpretations, Tarhn argues that Parmenides was not, after all, guilty of the confusion between the existential and copulative senses of "to be," that he did not identify thinking with Being, and that he had no conception of atemporal reality.~ In these and (...) other respects Tar~n's volume makes a valuable contribution to our understanding of Parmenides. One might judge, however, that Tars work is unusually insensitive to the religious element in Parmenides' poem, and in this respect his analysis seems to echo Reinhardt's unfortunate judgment which calls Parmenides "einen Denker, der keinen Wunsch kennt als Erkenntnis, keine Fessel ffihlt als Logik, den Gott und Geffihl gleichgiiltig lassen." s This inadequacy of TarAn's approach to Parmenides is evident in his treatment of the poem in general, and especially the prologue. The prologue to Parmenides' poem has always been a source of debate. After exploring and rejecting the allegorical interpretation of Sextus (the main source for the proem), Tar~n then systematically examines and rejects the modern interpretations which (among others) make it out to be a shamanistic rapture (Diels, Cornford), Orphic apocalypse (Burnet), religious revelation (Jaeger, Bowra), and mystical experience (Verdenius).4 TarAn judges that Parmenides did not intend his journey to be taken as a reality in any sense, largely on the grounds (1) that Parmenides speaks of his journey as a repeated experience. To take seriously the iterative expressions of the prologue (e.g. fr. 1, lines 1, 3, 8) is incompatible with interpretations which construe it to refer to a specific occasion.6 He supports the conclusion that the proem is nothing more than a literary device with the observations (2) that symbolic interpretations are incongruous with the fact that the goddess expounds her doctrine without symbols, and (3) that the appeal is to Logos, the rational, critical faculty; (4) that the goddess remains anonymous shows that she stands for no religious figure at all ("the 'revelation' is the truth discovered by Parmenides himself"); and (5) that Parmenides could hardly expect us to take seriously the reality of the goddess and other elements in the proem, the reality of which would be entirely incompatible with the thesis of the poem, viz. that reality is One and that all multiplicity and distinction is unreal. ~ z Parmenides: A Text with Translation, Commentary, and Critical Essays (Princeton, 1965). See my review of this work in The Classical Journal, LXII (1967),232ff. aParmenides und die Geschiehtc der griechischen Philosophic (Bonn, 1916),p. 256. 4TarGn,p. 17ft.Guthrie believes that Parmenides recognized an affinity between his search for truth, and his religious activity and mystical experience, and that he reflected this in his mystical-allegorical prologue (History of Greek Philosophy [Cambridge, 1965],II, 13). Guthrie was not, apparently, aware of Ta~n's work when he wrote his second volume; and on the matter of the prologue he favors the work of Mansfeld (Offenbarung des Parmenides und die menschlichc Welt [Assen, 1964],chap. IV), and Bowra ("The Proem of Parmenides," Classical Philology, XXXII [1987],97ff). Tar~n, p. 30. * P. 30f. [67] 68 HISTORY OF PHILOSOPHY It is probably true that interpretations which find all sorts of religious elements in the proem (and the poem as a whole) go too far. On the other hand, Tar~n gives the impression that Parmenides was nothing more than a pedantic academician, and in this respect he tends to sin in the opposite direction. First, the possible religious significance of the prologue does not depend on its being taken to refer to a literal experience; but even if it did, it need not refer to a specific event; and even if that were so, it is a little forced to exclude a specific event in view of the iterative expressions which may be no more than a function of poetic style. As for his second charge, Tar~n seems unaware that the main part of the poem hardly lends itself to symbolic expression, and afortiori the prologue, with its symbolism, sets the religious mood for... (shrink)

Smysl zhizni -- Statʹi raznykh let : Staryĭ i novyĭ nat︠s︡ionalʹnyĭ messianizm. Umozrenie v kraskakh. Dva mira v drevnerusskoĭ ikonopisi. "Inoe t︠s︡arstvo" i ego iskateli v russkoĭ narodnoĭ skazke.

At times, the academy seems devoid of justice because it emphasizes the cultivation of knowledge often denied to marginalized individuals and communities. As black queer feminist scholars doing praxis-driven theorizing from separate fields on the subject of black queer families and communities, we employ research methods that resist the dynamics of power and privilege that exist within normative researcher-participant exchanges. In this essay, we explore and highlight the ethical, justice-oriented, and dialogical relationship between researcher-scholars and research participants. Through story and (...) theory, we illustrate and argue that autoethnographies and narrative interviews can act as epistemological excavation tools for both researchers and participants, as they become sites of individual and collective consciousness. Our work resists capitalist models of research and instead promotes a justice-oriented and community-derived building of knowledge. (shrink)

We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with (...) degrees of categoricity is $\Pi_{1}^{1}$-complete. (shrink)