We study the problem of existence of maximal chains in the Turing degrees. We show that: 1. ZF+DC+"There exists no maximal chain in the Turing degrees" is equiconsistent with ZFC+"There exists an inaccessible cardinal"; 2. For all a ∈ 2ω.(ω₁)L[a] = ω₁ if and only if there exists a $\Pi _{1}^{1}[a]$ maximal chain in the Turing degrees. As a corollary, ZFC + "There exists an inaccessible cardinal" is equiconsistent with ZFC + "There is no (bold face) $\utilde{\Pi}{}_{1}^{1}$ maximal chain of (...) Turing degrees". (shrink)

We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey’s Theorem for Pairs.

Related Works: Part II: C. T. Chong, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part II: Tame $\Sigma_2$ Coding and the Jump Operator. Ann. Pure Appl. Logic, vol. 87, no. 2, 103--116. Mathematical Reviews : MR1490049 Part III: C. T. Chong, Lei Qian, Theodore A. Slaman, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part III: Prompt Sets, Minimal Paries and Shoenfield's Conjecture. Mathematical Reviews : MR1818378.

We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models. and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey's Theorem for Pairs.

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () and prove the following results: in any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle.

Background Residual dried blood spots (rDBS) from newborn screening programmes represent a valuable resource for medical research, from basic sciences, through clinical to public health. In Hong Kong, there is no legislation for biobanking. Parents’ view on the retention and use of residual newborn blood samples could be cultural-specific and is important to consider for biobanking of rDBS. Objective To study the views and concerns on long-term storage and secondary use of rDBS from newborn screening programmes among Hong Kong Chinese (...) parents. Methods A mixed-method approach was used to study the views and concerns on long-term storage and secondary use of rDBS from newborn screening programmes among Hong Kong Chinese parents of children 0–3 years or expecting parents through focus groups (8 groups; 33 participants) and a survey (n = 1012, 85% mothers) designed with insights obtained from the focus groups. We used framework analysis to summarise the themes as supportive factors, concerns and critical arguments for retention and secondary use of rDBS from focus group discussion. We used multiple logistic regression to assess factors associated with support for retention and secondary use of rDBS in the survey. Results Both in focus groups and survey, majority of parents were not aware of the potential secondary use of rDBS. Overall secondary use of rDBS in medical research was well accepted by a large proportion of Hong Kong parents, even if all potential future research could not be specified in a broad consent. However parents were concerned about potential risks of biobanking rDBS including leaking of data and mis-use of genetic information. Parents wanted to be asked for permission before rDBS are stored and mainly did not accept an “opt-out” approach. The survey showed that parents born in mainland China, compared to Hong Kong born parents, had lower awareness of newborn screening but higher support in biobanking rDBS. Higher education was associated with support in rDBS biobanking only among fathers. Conclusion Long-term storage and secondary use of rDBS from newborn screening for biomedical research and a broad consent for biobanking of rDBS are generally acceptable to Hong Kong parents given their autonomy is respected and their privacy is protected, highlighting the importance of an accountable governance and a transparent access policy for rDBS biobanks. (shrink)

During a pandemic, where there is widespread human infection, various and varying measures are taken that are targeted at public health objectives. During the early stages of a pandemic, these objectives may focus on containing the disease and minimizing its spread, but they may switch to mitigation as the emergent infectious disease takes hold in a population. There has been considerable debate and elucidation of the ethical principles and framework for the various responses including the need to fast track research (...) and vaccine development. However, the measures imposed during a pandemic would have unintended and untoward effect on ongoing clinical research. For example, precautionary measures, such as social distancing, may hamper ongoing clinical research, because recruitment and participation of patients and healthy volunteers is a potential source of virus spread. In this paper, we argue that a framework is needed to ensure the continuity of such research. Such a framework that considers the pertinent issues would need the ‘buy in’ of the key stakeholders (policy makers, funding agencies, institutional authorities, researchers and subjects) to ensure that the issues that are ethically relevant to pandemic planning would not be neglected or overlooked. (shrink)

A coordinate-free formulation is established for (semi) classical particle-field interactions. The exterior language of spacetime chains and De-Rham currents enables the description to include extended strings and membranes besides point particles. Treating physical fields in terms of sections of particular bundles, a unified account of interactions is presented in terms of an intrinsic action principle on a bundle of jets over spacetime. The theory is illustrated by considering the specific model of point particles with intrinsic spin covariantly coupled to theU(1) (...) andSL(2, C) connections describing the electromagnetic and gravitational fields, respectively. The notion of dual spin is examined in this context and coupled equations for this particle-field system are explicitly derived in a local chart. Attention is drawn to the global implications of the theory. (shrink)

We are told that when news of Caracalla's death reached Rome a group of senators denounced their former emperor, likening him to all the tyrants of the past who had ruled over them. The senator who recorded these actions, the historian Cassius Dio, does not say which tyrants were listed, but it is likely that such a comprehensive list included the last king of Rome, Tarquinius Superbus, and his son Sextus. The senators' actions were doubtless more an act of group (...) catharsis than a private show of loyalty to their new emperor, Marcus Opellius Macrinus. Yet what the scene reveals perhaps most clearly is the Romanexemplatradition in practice. (shrink)