Consider an axiomatic set theory in which there is a distinction between “sets” and “classes,” only sets being allowable as elements. How can one define a finite sequence of classes? This problem was proposed to me by A. Tarski, and a solution is given in this note. We shall assume the axiom system Σ used by Godei in his study of the continuum hypothesis, and shall use the same notation.1.

1. The theory of classes presented in this paper is a simplification of that presented by J. von Neumann in his paper Die Axiomatisierung der Mengenlehre. However, this paper is written so that it can be read independently of von Neumann's. The principal modifications of his system are the following.(1) The idea of ordered pair is defined in terms of the other primitive concepts of the system. (See Axiom 4.3 below.)(2) A much simpler proof of the well-ordering theorem, based on (...) von Neumann's equivalence axiom (Axiom 2.2 below) is given. (More exactly, the theory of ordinal numbers, on which the proof of the well-ordering theorem is based, is simplified—see §8.)(3) Functions are not assumed to be defined for all arguments. In place of “ = A” we have “is undefined.” This makes possible a constructive interpretation of the system. (See §2.)2. We wish first to give a rough picture of the system which we are trying to construct. Suppose that we have the idea “class,” but no material from which to construct classes. Nevertheless, we can construct the class 0 having no elements. And then the class 1 having 0 as its only element. And then the classes {1}, and {0, 1}, etc., using always the previously constructed classes as elements. To extend this method to infinite classes, we must give rules telling what elements are to be included. Since the nature of the rules which we can use is not altogether clear, we try to formalize the whole system; that is, to set up a system of axioms which seems to characterize this system of classes. Now in this set of axioms we find it necessary to use the idea of function (in the “Axiom of Replacement”). (shrink)

This study aims to examine the development of diversity and inclusion (D&I) literature and identify its prominent themes and blind spots. The research was conducted using bibliometric analysis on the Web of Science database and included 2510 publications. Results showed that the development of D&I literature had increased exponentially since the 1960s, mainly due to different political and societal events. The geographic development showed that research was primarily conducted in developed countries where quotas and other legislation are implemented. The thematic (...) development revealed a stable but narrow focus on diversity management, board diversity, and team diversity, with little attention to inclusion. The keyword analysis strongly emphasized surface-level diversity, such as gender, race, and cultural diversity, while deep-level diversity received less attention. This study concludes that previous D&I literature has mainly focused on the financial effects of D&I and neglected other elements, such as the effects on social performance, its ethical implications, and the relationship between diversity and inclusion. The study recommends future research to expand the interpretation of diversity, examine the relationship between diversity and inclusion, and explore the effects of diversity on non-financial outcomes such as social performance and ethics. This study provides a valuable contribution to the field of business ethics by highlighting the blind spots in D&I literature and encouraging future research to consider the ethical implications of diversity in the workplace. (shrink)

The present study tested the hypothesis that centrality of religiosity as defined as the position of an individual’s religious construct system in personality moderates the relationship between the experience of forgiveness by God and forgivingness for others. Participants completed measures of forgiveness by God, forgivingness, and centrality of religiosity. The moderating hypothesis was tested by treating centrality of religiosity both as a continuous variable and as a categorical variable with reference to a typological distinction. Results indicate that centrality of religiosity (...) moderates the positive relationship between forgiveness by God and forgivingness for others, implying that this relation only occurs if the religious construct system is in a central position in personality, but not if it is in a subordinate position. These results underline the importance of considering centrality of religiosity as an individual difference variable. (shrink)

The aim of this study was to analyze the association between physical activity and eating habits during the COVID-19 pandemic among Brazilian adults. A sample of 1,929 participants answered an online survey, however 1,874 were included in the analysis. The impact of the COVID-19 pandemic on eating habits was assessed inquiring about participants' intake of fruits, vegetables, fried foods, and sweets during the pandemic. Physical activity was assessed by asking participants about their weekly frequency, intensity and number of minutes/hours engaging (...) in structured physical activities per week. Participants were then stratified into categories based on moderate-to-vigorous intensity and into active or inactive. Increased sweets consumption was the most commonly reported change to eating habits, followed by an increase in the consumption of vegetables, fruits, and fried foods. Physical activity practice was related to lower consumption of fried foods and sweets. A cluster analysis revealed subjects with higher the level of physical activity was more likely to follow a healthy diet. Thus, physical activity was positively associated with healthier eating habits. Health authorities must recommend regular physical as a strategy to improve overall health during the COVID-19 pandemic. Future studies should address the physical activity interventions to improve health status during a pandemic. (shrink)

BackgroundThe outbreak of novel coronavirus disease 2019 has caused a global panic and public concern due to its mortality ratio and lack of treatments/vaccines. Reduced levels of physical activity have been reported during the outbreak, affecting the normal daily pattern.ObjectiveTo investigate the relationship of physical activity level with sleep quality and the effects of reduction physical activity levels on sleep quality.MethodsA Google form was used to address personal information, COVID-19 personal care, physical activity, and mental health of 1,907 adult volunteers. (...) Binary logistic regression was used to verify the association of physical activity parameters and sleep quality.ResultsInsufficient physical activity levels were a risk factor to have disturbed sleep pattern [OR: 1.28, 95% CI ]; however, when the BMI was added to the analysis, there was no more statistical difference [OR: 1.23, 95% CI ]. On the other hand, we found that the reduction of physical activity levels was associated with negative changes in sleep quality [OR: 1.73, 95% CI ], regardless all the confounders [OR: 1.30, 95% CI ], unless when feeling of depression was added in Model 6 [OR: 1.28, 95% CI ].ConclusionDisruption in daily physical activity routine, rather than physical activity level, negatively influences sleep quality during the COVID-19 quarantine. (shrink)

There is an increasing interest in how managers describe and respond to what they regard as moral versus nonmoral problems in organizations. In this study, forty managers described a moral problem and a nonmoral problem that they had encountered in their organization, each of which had been resolved. Analyses indicated that: (1) the two types of problems could be significantly differentiated using four of Jones' (1991) components of moral intensity; (2) the labels managers used to describe problems varied systematically between (...) the two types of problems and according to the problem's moral intensity; and (3) problem management processes varied according to the problem's type and moral intensity. (shrink)

Background: In Switzerland, non-medical right-to-die organisations such as Exit Deutsche Schweiz and Dignitas offer suicide assistance to members suffering from incurable diseases. Objectives: First, to determine whether differences exist between the members who received assistance in suicide from Exit Deutsche Schweiz and Dignitas. Second, to investigate whether the practices of Exit Deutsche Schweiz have changed since the 1990s. Methods: This study analysed all cases of assisted suicide facilitated by Exit Deutsche Schweiz (E) and Dignitas (D) between 2001 and 2004 and (...) investigated by the University of Zurich’s Institute of Legal Medicine (E: n = 147; D: n = 274, total: 421). Furthermore, data from the Exit Deutsche Schweiz study which investigated all cases of assisted suicide during the period 1990–2000 (n = 149) were compared with the data of the present study. Results: More women than men were assisted in both organisations (D: 64%; E: 65%). Dignitas provided more assistance to non-residents (D: 91%; E: 3%; p = 0.000), younger persons (mean age in years (SD): D: 64.5 (14.1); E: 76.6 (13.3); p = 0.001), and people suffering from fatal diseases such as multiple sclerosis and amyotrophic lateral sclerosis (D: 79%; E: 67%; p = 0.013). Lethal medications were more often taken orally in cases assisted by Dignitas (D: 91%; E: 76%; p = 0.000). The number of women and the proportion of older people suffering from non-fatal diseases among suicides assisted by Exit Deutsche Schweiz has increased since the 1990s (women: 52% to 65%, p = 0.031; mean age in years (SD): 69.3 (17.0) to 76.9 (13.3), p = 0.000), non-fatal diseases: 22% to 34%, p = 0.026). Conclusions: Weariness of life rather than a fatal or hopeless medical condition may be a more common reason for older members of Exit Deutsche Schweiz to commit suicide. The strong over-representation of women in both Exit Deutsche Schweiz and Dignitas suicides is an important phenomenon so far largely overlooked and in need of further study. (shrink)

Background: In Switzerland, non-medical right-to-die organisations such as Exit Deutsche Schweiz and Dignitas offer suicide assistance to members suffering from incurable diseases.Objectives: First, to determine whether differences exist between the members who received assistance in suicide from Exit Deutsche Schweiz and Dignitas. Second, to investigate whether the practices of Exit Deutsche Schweiz have changed since the 1990s.Methods: This study analysed all cases of assisted suicide facilitated by Exit Deutsche Schweiz and Dignitas between 2001 and 2004 and investigated by the University (...) of Zurich’s Institute of Legal Medicine. Furthermore, data from the Exit Deutsche Schweiz study which investigated all cases of assisted suicide during the period 1990–2000 were compared with the data of the present study.Results: More women than men were assisted in both organisations. Dignitas provided more assistance to non-residents, younger persons : D: 64.5 ; E: 76.6 ; p = 0.001), and people suffering from fatal diseases such as multiple sclerosis and amyotrophic lateral sclerosis. Lethal medications were more often taken orally in cases assisted by Dignitas. The number of women and the proportion of older people suffering from non-fatal diseases among suicides assisted by Exit Deutsche Schweiz has increased since the 1990s : 69.3 to 76.9, p = 0.000), non-fatal diseases: 22% to 34%, p = 0.026).Conclusions: Weariness of life rather than a fatal or hopeless medical condition may be a more common reason for older members of Exit Deutsche Schweiz to commit suicide. The strong over-representation of women in both Exit Deutsche Schweiz and Dignitas suicides is an important phenomenon so far largely overlooked and in need of further study. (shrink)