Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

Adopting a family approach to theory and practice: measuring distress in cancer patient-partner dyads with the distress thermometer

Objective: Significant others are central to patients' experience and management of their cancer illness. Building on our validation of the Distress Thermometer (DT) for family members, this investigation examines individual and collective distress in a sample of cancer patients and their matched partners, accounting for the aspects of gender and role. Method: Questionnaires including the DT were completed by a heterogeneous sample of 224 couples taking part in a multisite study. Results: Our investigation showed that male patients (34.2%), female patients (31.9%), and male partners (29.1%) exhibited very similar levels of distress, while female partners (50.5%) exhibited much higher levels of distress according to the DT. At the dyad level just over half the total sample contained at least one individual reporting significant levels of distress. Among dyads with at least one distressed person, the proportion of dyads where both individuals reported distress was greatest (23.6%). Gender and role analyses revealed that males and females were not equally distributed among the four categories of dyads (i.e. dyads with no distress; dyads where solely the patient or dyads where solely the partner is distressed; dyads where both are distressed). Conclusion: A remarkable number of dyads reported distress in one or both partners. Diverse patterns of distress within dyads suggest varying risks of psychosocial strain. Screening patients' partners in addition to patients themselves may enable earlier identification of risk settings. The support offered to either member of such dyads should account for their role- and gender-specific needs. Copyright © 2010 John Wiley ; Sons, Ltd.