"This is a timely collection of important papers.

This study will be of interest to anyone concerned with a critical appraisal of mental health service users’ and carers’ participation in research collaboration and with the potential of the postcolonial paradigm of cultural safety to contribute to the service user research (SUR) movement. The history and nature of the mental health field and its relationship to colonial processes provokes a consideration of whether cultural safety could focus attention on diversity, power imbalance, cultural dominance and structural inequality, identified as barriers (...) and tensions in SUR. We consider these issues in the context of state‐driven approaches towards SUR in planning and evaluation and the concurrent rise of the SUR movement in the UK and Australia, societies with an intimate involvement in processes of colonisation. We consider the principles and motivations underlying cultural safety and SUR in the context of the policy agenda informing SUR. We conclude that while both cultural safety and SUR are underpinned by social constructionism constituting similarities in principles and intent, cultural safety has additional dimensions. Hence, we call on researchers to use the explicitly political and self‐reflective process of cultural safety to think about and address issues of diversity, power and social justice in research collaboration. (shrink)

This collection by some of the leading scholars of Strauss's work is the first devoted to Strauss's thought regarding education. It seeks to address his conception of education as it applies to a range of his most important concepts, such as his views on the importance of revelation, his critique of modern democracy and the importance of modern classical education.

Let ω be the set of natural numbers. For functions f, g: ω → ω, we say f is dominated by g if f < g for all but finitely many n ∈ ω. We consider the standard “fair coin” probability measure on the space 2ω of in-finite sequences of 0's and 1's. A Turing oracle B is said to be almost everywhere dominating if, for measure 1 many X ∈ 2ω, each function which is Turing computable from X is (...) dominated by some function which is Turing computable from B. Dobrinen and Simpson have shown that the almost everywhere domination property and some of its variant properties are closely related to the reverse mathematics of measure theory. In this paper we exposit some recent results of Kjos-Hanssen, Kjos-Hanssen/Miller/Solomon, and others concerning LR-reducibility and almost everywhere domination. We also prove the following new result: If B is almost everywhere dominating, then B is superhigh, i. e., 0″ is truth-table computable from B ′, the Turing jump of B. (shrink)

We investigate the provability or nonprovability of certain ordinary mathematical theorems within certain weak subsystems of second order arithmetic. Specifically, we consider the Cauchy/Peano existence theorem for solutions of ordinary differential equations, in the context of the formal system RCA 0 whose principal axioms are ▵ 0 1 comprehension and Σ 0 1 induction. Our main result is that, over RCA 0 , the Cauchy/Peano Theorem is provably equivalent to weak Konig's lemma, i.e. the statement that every infinite {0, 1}-tree (...) has a path. We also show that, over RCA 0 , the Ascoli lemma is provably equivalent to arithmetical comprehension, as is Osgood's theorem on the existence of maximum solutions. At the end of the paper we digress to relate our results to degrees of unsolvability and to computable analysis. (shrink)

A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if every member of Q Turing computes a member of P. We say that P is strongly reducible to Q if every member of Q Turing computes a member of P via a fixed Turing functional. The weak degrees and strong degrees are the equivalence classes of mass problems under weak and strong reducibility, respectively. We (...) focus on the countable distributive lattices P w and P s of weak and strong degrees of mass problems given by nonempty Π 1 0 subsets of 2 ω . Using an abstract Gödel/Rosser incompleteness property, we characterize the Π 1 0 subsets of 2 ω whose associated mass problems are of top degree in P w and P s , respectively. Let R be the set of Turing oracles which are random in the sense of Martin-Löf, and let r be the weak degree of R. We show that r is a natural intermediate degree within P w . Namely, we characterize r as the unique largest weak degree of a Π 1 0 subset of 2 ω of positive measure. Within P w we show that r is meet irreducible, does not join to 1, and is incomparable with all weak degrees of nonempty thin perfect Π 1 0 subsets of 2 ω . In addition, we present other natural examples of intermediate degrees in P w . We relate these examples to reverse mathematics, computational complexity, and Gentzen-style proof theory. (shrink)

We investigate the reverse-mathematical status of several theorems to the effect that the natural number system is second-order categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i∈A and f:A→A. A subset X⊆A is said to be inductive if i∈X and ∀a ∈X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be (...) an inductive system such that f is one-to-one and i∉the range of f. The standard example of a Peano system is N,0,S where N={0,1,2,…,n,…}=the set of natural numbers and S:N→N is given by S=n+1 for all n∈N. Consider the statement that all Peano systems are isomorphic to N,0,S. We prove that this statement is logically equivalent to WKL0 over RCA0⁎ source. From this and similar equivalences we draw some foundational/philosophical consequences. (shrink)

Let CKDT be the assertion that for every countably infinite bipartite graph G, there exist a vertex covering C of G and a matching M in G such that C consists of exactly one vertex from each edge in M. (This is a theorem of Podewski and Steffens [12].) Let ATR0 be the subsystem of second-order arithmetic with arithmetical transfinite recursion and restricted induction. Let RCA0 be the subsystem of second-order arithmetic with recursive comprehension and restricted induction. We show that (...) CKDT is provable in ART0. Combining this with a result of Aharoni, Magidor, and Shore [2], we see that CKDT is logically equivalent to the axioms of ATR0, the equivalence being provable in RCA0. (shrink)

In this paper, we introduce a system of nonstandard second-order arithmetic $\mathsf{ns}$-$\mathsf{WWKL_0}$ which consists of $\mathsf{ns}$-$\mathsf{BASIC}$ plus Loeb measure property. Then we show that $\mathsf{ns}$-$\mathsf{WWKL_0}$ is a conservative extension of $\mathsf{WWKL_0}$ and we do Reverse Mathematics for this system.

Objective: The aim of this study was to examine the psychometric properties and factorial structure of the Schema Mode Inventory for Eating Disorders (SMI-ED) in a disordered eating population. Method: 573 participants with disordered eating patterns as measured by the Eating Disorder Examination Questionnaire (EDE-Q) completed the 190-item adapted version of the Schema Mode Inventory (SMI). The new SMI-ED was developed by clinicians/researchers specializing in the treatment of eating disorders, through combining items from the original SMI with a set of (...) additional questions specifically representative of the eating disorder population. Psychometric testing included Confirmatory Factor Analysis (CFA) and internal consistency (Cronbach’s α). Multivariate Analyses of Covariance (MANCOVA) was also run to test statistical differences between the EDE-Q subscales on the SMI-ED modes, while controlling for possible confounding variables. Results: Factorial analysis confirmed an acceptable sixteen-related-factors solution for the SMI-ED, thus providing preliminary evidence for the adequate validity of the new measure based on internal structure. Concurrent validity was also established through moderate to high correlations on the modes most relevant to eating disorders with EDE-Q subscales. This study represents the first step in creating a psychometrically sound instrument for measuring schema modes in eating disorders, and provides greater insight into the relevant schema modes within this population. Conclusion: This research represents an important preliminary step toward understanding and labeling the schema mode model for this clinical group. Findings from the psychometric evaluation of SMI-ED suggest that this is a useful tool which may further assist in the measurement and conceptualization of schema modes in this population. (shrink)

By , we denote the system of second-order arithmetic based on recursive comprehension axioms and Σ10 induction. is defined to be plus weak König's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. In this paper, we first show that for any countable model M of , there exists a countable model M′ of whose first-order part is the same as that of M, and whose second-order part consists of the M-recursive sets and sets not (...) in the second-order part of M. By combining this fact with a certain forcing argument over universal trees, we obtain the following result : if proves X!Y with arithmetical, so does . We also discuss several improvements of this results. (shrink)

We examine the concept of almost everywhere domination from the viewpoint of mass problems. Let AED and MLR be the sets of reals which are almost everywhere dominating and Martin-Löf random, respectively. Let b1, b2, and b3 be the degrees of unsolvability of the mass problems associated with AED, MLR × AED, and MLR ∩ AED, respectively. Let [MATHEMATICAL SCRIPT CAPITAL P]w be the lattice of degrees of unsolvability of mass problems associated with nonempty Π01 subsets of 2ω. Let 1 (...) and 0 be the top and bottom elements of [MATHEMATICAL SCRIPT CAPITAL P]w. We show that inf, inf, and inf belong to [MATHEMATICAL SCRIPT CAPITAL P]w and 0 < inf < inf < inf < 1. Under the natural embedding of the recursively enumerable Turing degrees into [MATHEMATICAL SCRIPT CAPITAL P]w, we show that inf and inf but not inf are comparable with some recursively enumerable Turing degrees other than 0 and 0′. In order to make this paper more self-contained, we exposit the proofs of some recent theorems due to Hirschfeldt, Miller, Nies, and Stephan. (shrink)

Let $\mathcal{P}_w$ be the lattice of Muchnik degrees of nonempty $\Pi^0_1$ subsets of $2^\omega$. The lattice $\mathcal{P}$ has been studied extensively in previous publications. In this note we prove that the lattice $\mathcal{P}$ is not Brouwerian.

A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F$_{\sigma}$ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measure-theoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some $\omega$-models of RCA$_0$which are relevant for the reverse mathematics of measure-theoretic regularity.

We consider implicit definability over the natural number system $\mathbb{N},+,\times,=$. We present a new proof of two theorems of Leo Harrington. The first theorem says that there exist implicitly definable subsets of $\mathbb{N}$ which are not explicitly definable from each other. The second theorem says that there exists a subset of $\mathbb{N}$ which is not implicitly definable but belongs to a countable, explicitly definable set of subsets of $\mathbb{N}$. Previous proofs of these theorems have used finite- or infinite-injury priority constructions. (...) Our new proof is easier in that it uses only a nonpriority oracle construction, adapted from the standard proof of the Friedberg jump theorem. (shrink)

Despite the challenges associated with virtually mediated communication, remote collaboration is a defining characteristic of online multiplayer gaming communities. Inspired by the teamwork exhibited by players in first-person shooter games, this study investigated the verbal and behavioral coordination of four-player teams playing a cooperative online video game. The game, Desert Herding, involved teams consisting of three ground players and one drone operator tasked to locate, corral, and contain evasive robot agents scattered across a large desert environment. Ground players could move (...) throughout the environment, while the drone operator’s role was akin to that of a “spectator” with a bird’s-eye view, with access to veridical information of the locations of teammates and the to-be-corralled agents. Categorical recurrence quantification analysis was used to measure the communication dynamics of teams as they completed the task. Demands on coordination were manipulated by varying the ground players’ ability to observe the environment with the use of game “fog.” Results show that catRQA was sensitive to changes to task visibility, with reductions in task visibility reorganizing how participants conversed during the game to maintain team situation awareness. The results are discussed in the context of future work that can address how team coordination can be augmented with the inclusion of artificial agents, as synthetic teammates. (shrink)

Day length provides an important environmental cue by signalling conditions favourable for flowering. While Arabidopsis promotes flowering in response to long days, rice promotes flowering in response to short days. Despite this difference, a recent paper reveals that the network controlling this response is highly conserved in these distantly related plants, only the activity of one component is reversed.1 This reveals how an important developmental process can be diversified for adaptation by using the same set of genes, but regulating them (...) differently. BioEssays 25:829–832, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

uppose that the most fundamental and general principle of a science had been known for over a century and had long since become a main basis for understanding and research by scientists in that field. You would surely assume that the principle would be taken as a matter of course by everyone with even a nodding acquaintance with the science. It would obviously be taught everywhere as basic to the science at any level of education. If you think that about (...) biology, however, you are wrong. (shrink)

In debates over the regulation of communication related to dual-use research, the risks that such communication creates must be weighed against against the value of scientific autonomy. The censorship of such communication seems justifiable in certain cases, given the potentially catastrophic applications of some dual-use research. This conclusion however, gives rise to another kind of danger: that regulators will use overly simplistic cost-benefit analysis to rationalize excessive regulation of scientific research. In response to this, we show how institutional design principles (...) and normative frameworks from free speech theory can be used to help extend the argument for regulating dangerous dual-use research beyond overly simplistic cost-benefit reasoning, but without reverting to an implausibly absolutist view of scientific autonomy. (shrink)

We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive (...) on open sets. (shrink)