S. Ulam asked about the number of nonisomorphic projective algebras with k generators. This paper answers his question for projective algebras of finite dimension at least three and shows that there are the maximum possible number, continuum many, of nonisomorphic one-generated structures of finite dimension n, where n is at least three, of the following kinds: projective set algebras, projective algebras, diagonal-free cylindric set algebras, diagonal-free cylindric algebras, cylindric set algebras, and cylindric algebras. The results of this paper extend earlier (...) results to the collection of cylindric set algebras and provide a uniform proof for all the results. Extensions of these results for dimension two are discussed where some modifications on the hypotheses are needed. Furthermore for α |geq 2, the number of isomorphism classes of regular locally finite cylindric set algebras of dimension α of the following two kinds are computed: ones of power κ for infinite $\kappa \geq|\alpha|$ , and ones with a single generator. (shrink)

The goal of this short note is to interest set theorists in the order type ω*ω1, and to encourage them to work on the question of whether or not the Continuum Hypothesis decides the partition relation τ→2, for τ=ω*ω1 and for τ=ω1ω+2.

Suppose that α = γ + δ where $\gamma \geq \delta > 0$ . Then there is a graph G = (ω ω α ,E) which has no independent set of order type ω ω α and has no pentagram (a pentagram is a set of five points with all pairs joined by edges). In the notation of Erdos and Rado, who generalized Ramsey's Theorem to this setting, $\omega^{\omega^\alpha} \nrightarrow (\omega^{\omega^\alpha},5)^2.$.

Countable homogeneous relational structures have been studied by many people. One area of focus is the Ramsey theory of such structures. After a review of background material, a partition theorem of Laflamme, Sauer, and Vuksanovic for countable homogeneous binary relational structures is discussed with a focus on the size of the set of unavoidable colors.

Global stewardship explores the perspective of caring for the entire globe—all its peoples and life. The interconnectedness of the basic elementary systems—air and water, which are both necessary for terrestrial and aquatic life—is acknowledged. The concomitant threats of their toxification from immoderate employments of substances and techniques justify the need for global respect and cooperation as well as effective world economic systems as the means to sustain this life.

The aim of this essay is to examine the long-term evolution of the material reproductive vehicles of society. The fairly continuous trend of economic integration and progressive enfranchisement of the world’s people is indicated, ascertainable even with the emergence from general slavery of ancient times, through feudalism to the modern stage of industrialism and widespread national sovereignties. With greater political expression has come higher degrees and penetration of economic prosperity. Both vicious and virtuous tendencies of automation are considered. The necessary (...) foundation of living labor is recognized. (shrink)

This essay presents what is enduring and still powerful in Marx’s analysis of capital, viewed synthetically as the resulting moral imperative to fairness in the social relationships of production.

Integral Science provides the empirical rigor needed to shift medicine's worldview. The shift in science will give rise to Integral Medicine, which will emerge from the integration and transformational change of biomedicine, psychosocial approaches, Complementary and Alternative Medicine, and other reform movements. The root metaphor of Integral Medicine is a healthy and sustainable ecosystem. At its heart are mind-body holism and collaborative learning. Healing and the creation of health will emphasize educational, self-care, and community support models. Implications are discussed for (...) practice, research, and education. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Gendered Community: Rousseau, Sex, and PoliticsJean A. PerkinsGendered Community: Rousseau, Sex, and Politics, by Penny A. Weiss; xvii & 189 pp. New York: New York University Press, 1993, $40.00.As Penny Weiss puts it herself: “The main argument of this book is that Rousseau’s defense of sexual differentiation is based on the contribution he perceives it can make to the establishment of community” (p. 7). She accomplishes this by (...) dividing the work into two parts, the first devoted to an analysis of Rousseau’s Emile and Du Contrat social, the second consisting of two feminist essays inspired by her findings.After an introduction Weiss moves directly to an analysis of Emile, showing quite conclusively that the education given to Emile and Sophie does not differ in principle although it does differ in practice since the aim in both cases is to produce sex differences that will make each of them useful members of society. Chapter Three argues that, whereas Rousseau uses much of the rhetoric of innate and natural differences between the sexes, he really does not believe in this thesis. To Rousseau human nature, either male or female, is infinitely malleable. Chapter Four outlines the political benefits that Rousseau saw in the creation of a sex-roled affectionate family. The next chapter attempts to show the consistency of Rousseau’s thought, briefly described as nonliberal, anti-feminist, and communitarian. Up to this point Weiss has remained within the tradition of textual exegesis, but in Chapter Six she moves to a feminist critique of Rousseau’s thought. The argument put forward here is that sex-differentiated roles undermine community since it denies equality to the sexes. The eventual result of such a community would be the rampant spread of domination and the inevitable abuses of power this entails.This reviewer finds many problems with the book. An annoying trait is that the arguments are not given in logical order. For instance, human beings are described as asocial, indolent, and malleable before the author refers to the state of nature where Rousseau develops this idea. At no point does Weiss refer to the so-called Golden Age that intervenes in Rousseau’s scheme between the state of nature and civilization. In many ways this was Rousseau’s real ideal and his construct of an alternative society was only developed because it is impossible to go back to a previous developmental stage. Another, more grievous omission is the total lack of reference to La Nouvelle Héloïse. As William Ray has put it in a recent article, “I consider Julie and Emile as two stages of a single pedagogical project.” Perhaps Weiss, as a political scientist, does not believe that fictional works should be studied in the same way as treatises. Finally, there is an almost complete lack of references to critical works by literary critics (the exception is Jean Starobinski). Had Weiss been aware of Lester Crocker’s important works on Rousseau, she would not have been so surprised at his antifeminism or his recourse to manipulation in both education and society. The tutor or legislator need to arrange things so that individuals can perceive themselves to be free. [End Page 184]Chapters Two, Three, and Four offer the reader a careful look at Rousseau’s aims and methods. Chapter Five gives possible replies that Rousseau might have given in the face of certain criticisms. Chapters Six, Seven, and Eight are interesting from a feminist perspective. Despite its limitations Weiss’s book contains much that is useful and thought-provoking.Jean A. PerkinsSwarthmore CollegeCopyright © 1995 The Johns Hopkins University Press... (shrink)

This book presents a collection of contemporary discourses that reconsider the relationship of democracy as a political ideology and American ideal and education as the foundation of preparing democratic citizens in America.

BackgroundThe increased risk of developing attention-deficit hyperactivity disorder (ADHD) in extremely preterm infants is well-documented. Better understanding of perinatal risk factors, particularly those that are modifiable, can inform prevention efforts.MethodsWe examined data from the Extremely Low Gestational Age Newborns (ELGAN) Study. Participants were screened for ADHD at age 10 with the Child Symptom Inventory-4 (N = 734) and assessed at age 15 with a structured diagnostic interview (MINI-KID) to evaluate for the diagnosis of ADHD (N = 575). We studied associations (...) of pre-pregnancy maternal body mass index (BMI), pregestational and/or gestational diabetes, maternal smoking during pregnancy (MSDP), and hypertensive disorders of pregnancy (HDP) with 10-year and 15-year ADHD outcomes. Relative risks were calculated using Poisson regression models with robust error variance, adjusted for maternal age, maternal educational status, use of food stamps, public insurance status, marital status at birth, and family history of ADHD. We defined ADHD as a positive screen on the CSI-4 at age 10 and/or meeting DSM-5 criteria at age 15 on the MINI-KID. We evaluated the robustness of the associations to broadening or restricting the definition of ADHD. We limited the analysis to individuals with IQ ≥ 70 to decrease confounding by cognitive functioning. We evaluated interactions between maternal BMI and diabetes status. We assessed for mediation of risk increase by alterations in inflammatory or neurotrophic protein levels in the first week of life.ResultsElevated maternal BMI and maternal diabetes were each associated with a 55–65% increase in risk of ADHD, with evidence of both additive and multiplicative interactions between the two exposures. MSDP and HDP were not associated with the risk of ADHD outcomes. There was some evidence for association of ADHD outcomes with high levels of inflammatory proteins or moderate levels of neurotrophic proteins, but there was no evidence that these mediated the risk associated with maternal BMI or diabetes.ConclusionContrary to previous population-based studies, MSDP and HDP did not predict ADHD outcomes in this extremely preterm cohort, but elevated maternal pre-pregnancy BMI, maternal diabetes, and perinatal inflammatory markers were associated with increased risk of ADHD at age 10 and/or 15, with positive interaction between pre-pregnancy BMI and maternal diabetes. (shrink)

"In this groundbreaking book Jean Walton subjects psychoanalysis to a sustained and highly illuminating ethnographic critique.

Positive claims about narrative approaches to healthcare suggest they could have many benefits, including supporting person-centred healthcare (PCH). Narrative approaches have also been criticised, however, on both theoretical and practical grounds. In this paper we draw on epistemological work on narrative and knowledge to develop a conception of narrative that responds to these concerns. We make a case for understanding narratives as accounts of events in which the way each event is described as influenced by the ways other events in (...) the narrative are described. This view of narratives recognises that they can contribute knowledge of different kinds of connections between events: not just causal, and not just of patient’s perspectives. Additionally, narratives can add further epistemic value by suggesting potentially useful lines of inquiry. We take narrative approaches to healthcare to include clinicians considering both patients’ informational offerings and their own professional understandings as narratives. On this understanding, our account is able to overcome the major theoretical and practical criticisms that have been levelled against the use of narrative approaches in healthcare, and can help to explain why and how narrative approaches are consistent with PCH. (shrink)

Evidence in medicine can come from more or less trustworthy sources and be produced by more or less reliable methods, and its interpretation can be disputed. As such, it can be unclear when disagreements in medicine result from different, but reasonable, interpretations of the available evidence and when they result from unreasonable refusals to consider legitimate evidence. In this article, we seek to show how assessments of the relevance and implications of evidence are typically affected by factors beyond that evidence (...) itself, such as our beliefs about the credibility of the speaker or source of the evidence. In evaluating evidence, there is thus a need for reflective awareness about why we accept or dismiss particular claims. (shrink)