The uniqueness of the fixed-point in every diagonalizable algebra

Summary It is well known that, in Peano arithmetic, there exists a formulaTheor (x) which numerates the set of theorems. By Gödel's and Löb's results, we have that Therefore, the considered «equations» admit, up to provable equivalence, only one solution.In this paper we prove (Corollary 1), that, in general, ifP (x) is an arbitrary formula built fromTheor (x), then the fixed-point ofP (x) (which exists by the diagonalization lemma) is unique up to provable equivalence. This result is settled referring to the concept of diagonalizable algebra (see Introduction).The algebraization of the theories which express TheorAllatum est die 3 Augustii 1975     

Endocrinology of menopausal transition and its brain implications

The central nervous system is one of the main target tissues for sex steroid hormones, which act on both through genomic mechanisms, modulating synthesis, release, and metabolism of many neuropeptides and neurotransmitters, and through non-genomic mechanisms, influencing electrical excitability, synaptic function, morphological features, and neuron-glia interactions. During the climacteric period, sex steroid deficiency causes many neuroendocrine changes. At the hypothalamic level, estrogen withdrawal gives rise to vasomotor symptoms, to eating behavior disorders, and altered blood pressure control. On the other hand, at the limbic level, the changes in serotoninergic, noradrenergic, and opioidergic tones contribute to the modifications in mood, behavior, and nociception. Hormone replacement therapy (HRT) positively affects climateric depression throughout a direct effect on neural activity and on the modulation of adrenergic and serotoninergic tones and may modulate the decrease in cognitive efficiency observed in climaterium. The identification of the brain as a de novo source of neurosteroids, suggests that the modifications in mood and cognitive performances occurring in postmenopausal women may also be related to a change in the levels of neurosteroids. These findings open new perspectives in the study of the effects of sex steroids on the central nervous system and on the possible use of alternative and/or auxiliary HRT.     

Translating the hypergame paradox: Remarks on the set of founded elements of a relation

In Zwicker (1987) the hypergame paradox is introduced and studied. In this paper we continue this investigation, comparing the hypergame argument with the diagonal one, in order to find a proof schema. In particular, in Theorems 9 and 10 we discuss the complexity of the set of founded elements in a recursively enumerable relation on the set N of natural numbers, in the framework of reduction between relations. We also find an application in the theory of diagonalizable algebras and construct an undecidable formula.     

Writing as a meaningful activity

Writing processes have been studied extensively from the cognitive point of view, but little attention has been given to the affective aspects of this activity. In fact, writing experience seems to be relevant to a person not only because it is a complex cognitive activity, but also because it often has an affective characterization. The aim of the present study was to investigate writing as a meaningful activity, that is, to analyze the way in which pupils of different grade levels construe this activity. The study was divided into two phases: (a) interviews with pupils in order to select relevant elements (i.e., writing situations and contexts) and (b) subjects' elicitation of constructs and evaluation of elements. From the qualitative and quantitative analyses of the grids, a developmental trend emerged. Whereas the younger subjects frequently elicited constructs related to the affective dimension of writing, as age increased, the cognitive dimension became more evident.     

Methods of Cheating and Deterrents to Classroom Cheating: An International Study

This study examines the methods students use to cheat on class examinations and suggests ways of deterring using an international sample from Australia, China, Ireland, and the United States. We also examine the level of cheating and reasons for cheating that prior research has highlighted as a method of demonstrating that our sample is equivalent to those in prior studies. Our results confirm the results of prior research that primarily employs students from the United States. The data indicate that actions such as having multiple versions of the examination and scrambling the questions on these versions would deter cheating. In addition, given the increased level of cheating and students' increased perception of the social acceptability of cheating in college, the data provided by our international sample also suggest that some relatively simple precautions by instructors could dramatically reduce the level of cheating on in-class examinations.     

Book Reviews

Abstract

This article reports on a comparison of the views of teachers in Italy and the United Kingdom on their profession in relation to other professions. Common constructs about their profession are discussed for each national group, followed by a commentary on the similarities and differences between the groups related to their embedding culture. For example, both groups perceive teachers as having much in common with social workers and the clergy in terms of high demand for emotional involvement and creativity, while both express concern over low income for effort conjoined with erosion of professional autonomy. This latter concern is more pronounced in the data from Italy, reflecting the more centralized control of curriculum, a policy only currently being initiated in the United Kingdom

Although we are sympathetic to the reservations of Yorke (1987) about their utility in the study of teachers' thinking (as noted in Pope [1981] and Denicolo [1985]), we found the grid procedure to be a useful vehicle for exploring the issues in this study. Thus we have avoided treating the grid data in an essentially positivistic manner and did use notes made during the conversations that occurred during grid completion to shed light on the personal meaning to the participant of the words used to denote each construct. Within this article the details of personal meanings of each participant are omitted, although the analysis and discussion took account of these, since our particular goal here is to present the group data for the two countries.

The focus had been on the teachers' constructs regarding the teaching profession. The same data could be used to illuminate their views on any of the professions discussed in the study. In addition to developing insights into teachers' thinking about their profession, the study helped to strengthen the developing spirit of international collaboration in research in teacher education from the perspective of personal construct psychology.     

Better versus worse family therapy sessions as reflected in clients' alliance-related behavior

To be responsive to clients' evaluations of the unfolding therapy process, therapists must first accurately "read" client behavior, a particularly challenging task in conjoint family therapy. In this study, the authors compared client behavior in 28 sessions that one family member and the therapist concurred, on the Session Evaluation Questionnaire (W. B. Stiles & J. S. Snow, 1984), were relatively better or worse than their other sessions. Client behavior was rated from videotapes using the System for Observing Family Therapy Alliances (SOFTA-o; M. L. Friedlander et al., 2006). In contrast to the worse sessions, the better sessions were characterized by significantly greater client Engagement in the Therapeutic Process and Safety within the Therapeutic System. Notably, whereas only the worse sessions had exceptionally poor within-family collaboration, 40% of the better sessions were characterized by mild family conflict. Implications are discussed for building theory on therapist responsiveness and for future research that may benefit practice, training, and supervision.     

Violence and Latin‐American preadolescents: A study of social brain function and cortisol levels

The present study investigated exposure to violence and its association with brain function and hair cortisol concentrations in Latin‐American preadolescents. Self‐reported victimization scores (JVQ‐R2), brain imaging (fMRI) indices for a social cognition task (the ‘eyes test’), and hair cortisol concentrations were investigated, for the first time, in this population. The eyes test is based on two conditions: attributing mental state or sex to pictures of pairs of eyes (Baron‐Cohen, Wheelwright, Hill, Raste, & Plumb, 2001). The results showed an association among higher victimization scores and (a) less activation of posterior temporoparietal right‐hemisphere areas, in the mental state condition only (including right temporal sulcus and fusiform gyrus); (b) higher functional connectivity indices for the Amygdala and Right Fusiform Gyrus (RFFG) pair of brain regions, also in the mental state condition only; (c) higher hair cortisol concentrations. The results suggest more exposure to violence is associated with significant differences in brain function and connectivity. A putative mechanism of less activation in posterior right‐hemisphere regions and of synchronized Amygdala: RFFG time series was identified in the mental state condition only. The results also suggest measurable effects of exposure to violence in hair cortisol concentrations, which contribute to the reliability of self‐reported scores by young adolescents. The findings are discussed in light of the effects of exposure to violence on brain function and on social‐cognitive development in the adolescent brain. A video abstract of this article can be viewed at https://www.youtube.com/watch?v=qHcXq7Y9PBk