We continue [4] and study sets in generic extensions by the Magidor forcing and by the Prikry forcing with non-normal ultrafilters.

In this paper, we answer a question asked in Koepke et al. regarding a Mathias criteria for Tree-Prikry forcing. Also we will investigate Prikry forcing using various filters. For completeness and self inclusion reasons, we will give proofs of many known theorems.

We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin’s property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly strengthened forms, and present models with varying structures of the cofinal types of ultrafilters over measurable cardinals.

Very few data exist in France on: (1) nurses’ knowledge and behaviour concerning ethical decisions in clinical practice; and (2) their knowledge of ethical rules in clinical research. This questionnaire-based audit tried mainly to assess these questions in a large French university teaching hospital. Of the 257 questionnaires distributed to nurses in 23 clinical units of the hospital, 206 were returned (80% response rate). When responding to the vignette describing a clinical situation requiring an ethical decision to be made, most (...) nurses acted as the patient’s advocate although they have had no formal training in ethics. Indeed, 66% of nurses responding considered that the patients themselves should be the primary decision makers in situations that relate to their health and medical care. For children or comatose patients, the decision should be left to the relatives according to 72% of the responses. The results indicated that the role of health care professionals in ethical decisions made for a given patient should be marginal. Nurses’ knowledge concerning research protocols, particularly their ethical requirements and consequences, is poor at present and information from and communication with doctors should be improved. (shrink)

We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Theorem 2.3].

Abstract(1)We show that it is possible to add $\kappa ^+$ -Cohen subsets to $\kappa $ with a Prikry forcing over $\kappa $. This answers a question from [9].(2)A strengthening of non-Galvin property is introduced. It is shown to be consistent using a single measurable cardinal which improves a previous result by S. Garti, S. Shelah, and the first author [5].(3)A situation with Extender-based Prikry forcings is examined. This relates to a question of H. Woodin.

Journal of Mathematical Logic, Ahead of Print. We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Theorem 2.3].

We study which [Formula: see text]-distributive forcing notions of size [Formula: see text] can be embedded into tree Prikry forcing notions with [Formula: see text]-complete ultrafilters under various large cardinal assumptions. An alternative formulation — can the filter of dense open subsets of a [Formula: see text]-distributive forcing notion of size [Formula: see text] be extended to a [Formula: see text]-complete ultrafilter.

In der vorliegenden Arbeit wird ein Begriffsrahmen entwickelt, in dem sich Gemeinsamkeiten und Unterschiede zwischen drei Arten von Kulturprodukten klar aufzeigen lassen: Dichtung, Mythos und Wissenschaft. Die allen drei Phänomenen gemeinsame Struktur erfassen wir in §II und §III mit dem Begriff eines Repräsentationssystems, welcher in Anlehnung an die formale Modelltheorie semiotische Vorstellungen mit einem Denken in Systemen zusammenbringt. Die relevanten Unterschiede werden durch Differenzierung (§IV) jenes Begriffs festgemacht, d.h. die drei Phänomene werden durch jeweils spezielle Arten von Repräsentationssystemen erfaßt (§V). (...) Unser spezielles Augenmerk gilt dabei dem Mythos (§I), der sich in letzter Zeit eines wachsenden Interesses -- oft außerhalb des etablierten Wissenschaftsbetriebs -- erfreut. Es zeigt sich, daß der Mythos eine Mittelstellung zwischen Dichtung und Wissenschaft einnimmt: als "Bindeglied" vermittelt er sowohl zwischen der rein begrifflichen Struktur der Phänomene "Dichtung" und "Wissenschaft" als auch zwischen deren Unterschieden in Methode und Wahrheitsanspruch (die in engem Zusammenhang mit der begrifflichen Struktur stehen). Der hier entwickelte begriffliche Rahmen soll in weiteren Untersuchungen als Grundlage zur Herausarbeitung von Unterschieden in der Methode und im Wahrheitsanspruch dienen, die sich aus unserem Ansatz in natürlicher Weise ergeben. Diese müssen jedoch aus Platzgründen einer weiteren Arbeit vorbehalten bleiben. (shrink)

Journal of Mathematical Logic, Volume 24, Issue 03, December 2024. We study which [math]-distributive forcing notions of size [math] can be embedded into tree Prikry forcing notions with [math]-complete ultrafilters under various large cardinal assumptions. An alternative formulation — can the filter of dense open subsets of a [math]-distributive forcing notion of size [math] be extended to a [math]-complete ultrafilter.

We investigate two formalizations of Optimality Theory, a successful paradigm in linguistics.We first give an order-theoretic counterpart for the data and processinvolved in candidate evaluation.Basically, we represent each constraint as a function that assigns every candidate a degree of violation.As for the second formalization, we define (after Samek-Lodovici and Prince) constraints as operations that select the best candidates out of a set of candidates.We prove that these two formalizations are equivalent (accordingly, there is no loss of generality with using violation (...) marks and dispensing with them is only apparent).Importantly, we show that the second formalization is equivalent with a class of operations over sets of formulas in a given logical language.As a result, we prove that Optimality Theory can be characterized by certain cumulative logics.So, applying Optimality Theory is shown to be reasoning by the rules of cumulative logics. (shrink)

Aim Facebook is an increasingly popular online social networking site. The purpose of this study was to describe the Facebook activity of residents and fellows and their opinions regarding the impact of Facebook on the doctor–patient relationship. Methods An anonymous questionnaire was emailed to 405 residents and fellows at the Rouen University Hospital, France, in October 2009. Results Of the 202 participants who returned the questionnaire (50%), 147 (73%) had a Facebook profile. Among responders, 138 (99%) displayed their real name (...) on their profile, 136 (97%) their birthdates, 128 (91%) a personal photograph, 83 (59%) their current university and 76 (55%) their current position. Default privacy settings were changed by 61% of users, more frequently if they were registered for >1 year (p=0.02). If a patient requested them as a ‘friend’, 152 (85%) participants would automatically decline the request, 26 (15%) would decide on an individual basis and none would automatically accept the request. Eighty-eight participants (48%) believed that the doctor–patient relationship would be altered if patients discovered that their doctor had a Facebook account, but 139 (76%) considered that it would change only if the patient had open access to their doctor's profile, independent of its content. Conclusions Residents and fellows frequently use Facebook and display personal information on their profiles. Insufficient privacy protection might have an impact the doctor–patient relationship. (shrink)

A new formulation of the cusp catastrophe is used to model the fundamental biological functions of predation and reproduction. This new representation lies on the decomposition of the overall cusp potential in two component potentials individualising the conflicting pregnances. It results in a more accurate and less problematic description than the original proposition by R. Thom, mostly due to the use of parameters with strong physical and evocative power. For instance, it gives a very suggestive account for such biologically significant (...) processes as digestion and assimilation, or pregnancy and delivery. Two couples of parameters are used in the new representation of the cusp: one defines the exact shape of the conflicting attractors which symbolises genetic coding, the other controls the deformation of -and interaction between- the two attractors and represent hormonal effects. This new description strikingly echoes Heidegger's philosophical thought on ontological difference, by giving a representation of the distinct concepts of entity and Being. It thus precludes a previous criticism concerning the impossibility for catastrophic models to depict the entity level. Such a type of representation might be useful in translating syntactical-semantic models of catastrophe theory into computer language. (shrink)

Rationale, aims and objectives This randomized controlled trial was designed to evaluate the 2-year costs and effects of a proactive, public health nursing case management approach compared with a self-directed approach for 129 single parents (98% were mothers) on social assistance in a Canadian setting. A total of 43% of these parents had a major depressive disorder and 38% had two or three other health conditions at baseline. Methods Study participants were recruited over a 12 month period and randomized into (...) two groups: one receiving proactive public health nursing and one which did not. Results At 2 years, 69 single parents with 123 children receiving proactive public health nursing (compared with 60 parents with 91 children who did not receive public health nursing services) showed a slightly greater reduction in dysthymia and slightly higher social adjustment. There was no difference between the public health and control groups in total per parent annual cost of health and support services. However, costs were averted due to a 12% difference in non-use of social assistance in the previous 12 months for parents in the public health nursing group. This translates into an annual cost saving of $240 000 (Canadian) of costs averted within 1 year for every 100 parents. Conclusions In the context of a system of national health and social insurance, this study supports the fact that it is no more costly to proactively service this population of parents on social assistance. (shrink)

Standard quantum theory is inadequate to explain the mechanisms by which potential becomes actual. It is inadequate and therefore unable to describe generation of events. Niels Bohr emphasized long ago that the classical part of the world is necessary. John Bell stressed the same point: that “measurement≓ cannot even be defined within the standard quantum theory, and he sought a solution within hidden variable theories and his concept of “beables.≓Today it is customary to try to explain emergence of the classical (...) world through a decoherence mechanism due to “environment.≓ But, we believe, as it was with the concept of measurement, “environment≓ itself cannot be defined within the standard quantum theory.We have proposed a semiphenomenological solution to this problem by introducing explicitly, from the very beginning, classical degrees of freedom, and by coupling these degrees of freedom, through a Lindblad type coupling, to the quantum world. The resulting theory, we call “event-enhanced quantum theory.≓ EEQT allows us to describe an event-generating mechanism for individual quantum systems under continuous observation. The objections of John Bell are met and precise definitions of an “experiment≓ and of a “measurement≓ have been given within EEQT. However EEQT is, essentially, a nonrelativistic theory.In the present paper we extend the ideas of L. P. Horwitz and C. Piron and we propose a relativistic version of EEQT, with an event-generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relalivistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are nonnegative. (shrink)