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Objectives: Children and adolescents who were born very preterm (≤32 weeks’ gestation) are vulnerable to experiencing cognitive problems, including in executive function. However, it remains to be established whether cognitive deficits are evident in adulthood and whether these exert a significant effect on an individual’s real-lifeachievement. Methods: Using a cross-sectional design, we tested a range of neurocognitive abilities, with a focus on executive function, in a sample of 122 very preterm individuals and 89 term-born controls born between 1979 and 1984. Associations between executive function and a range of achievement measures, indicative of a successful transition to adulthood, were examined. Results: Very preterm adults performed worse compared to controls on measures of intellectual ability and executive function with moderate to large effect sizes. They also demonstrated significantly lower achievement levels in terms of years spent in education, employment status, and on a measure of functioning in work and social domains. Results of regression analysis indicated a stronger positive association between executive function and real-life achievement in the very preterm group compared to controls. Conclusions: Very preterm born adults demonstrate executive function impairments compared to full-term controls, and these are associated with lower achievement in several real-life domains. (JINS, 2017, 23, 381–389)

This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program promoted by Friedman and Simpson. We look in particular at: (i) the long arc from Poincaré to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent to Weak König’s Lemma, and (iv) the large-scale intellectual backdrop to arithmetical transfinite recursion in descriptive set theory and its effectivization by Borel, Lusin, Addison, and others.

Frege’s Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem (Theorem 2.9) shows that there is a model of a fragment of the Grundgesetze which defines a model of all the axioms of Zermelo–Fraenkel set theory with the exception of the power set axiom. The proof of this result appeals to Gödel’s constructible universe of sets and to Kripke and Platek’s idea of the projectum, as well as to a weak version of uniformization (which does not involve knowledge of Jensen’s fine structure theory). The axioms of the Grundgesetze are examples of abstraction principles, and the other primary aim of this paper is to articulate a sufficient condition for the consistency of abstraction principles with limited amounts of comprehension (Theorem 3.5). As an application, we resolve an analogue of the joint consistency problem in the predicative setting.

A semantics for quantified modal logic is presented that is based on Kleene’s notion of realizability. This semantics generalizes Flagg’s 1985 construction of a model of a modal version of Church’s Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church’s Thesis and a variant of a modal set theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra’s generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott’s graph model (for the untyped lambda calculus) which witnesses the failure of the stability of nonidentity.

Defect formation in the samples of graphene, graphene oxide and silicon irradiated with Ar cluster and highly-charged ion irradiations were studied. Ar cluster ions, with acceleration energy E = 30 kV (Exogenesis nAccel00, Boston, USA) and total Ar cluster ion fluences ranged from 1x109 cm-2 to 1x1013 cm-2 were directed toward various surfaces. Highly-charged ions (HCI) bombardment on surfaces with highly charged Xeq+ (q = 22) was employed at Eurasian National University, Kazakhstan, using a DC-60 cyclotron accelerator. Multi-layer graphene oxide, single-layer graphene- (SLG), few-layer of graphene (FLG) and polished Si are used for irradiation experiments. The study of irradiated samples was conducted by Raman spectroscopy, atomic force microscopy (AFM). Uniformly distributed defects and craters were observed on the surfaces of graphene, graphene oxide and silicon irradiated with cluster and HCI beams in our experiments. Ab-initio density-functional theory (DFT) was used to study point defects and molecular-dynamics (MD) simulations were used for studying formation of craters due to gas cluster ion impacts in graphene. The results of simulations were compared with experimental craters and surface shape.

Frege’s theorem says that second-order Peano arithmetic is interpretable in Hume’s Principle and full impredicative comprehension. Hume’s Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law V from Frege’s Grundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence relations in a weak background second-order logic. We show that this predicative Fregean theory interprets second-order Peano arithmetic (cf. Theorem 3.2).

Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory (Parsons, 1990; Parsons, 2008, sec. 49; McGee, 1997; Lavine, 1999; Väänänen & Wang, 2014). Another great enterprise in contemporary philosophy of mathematics has been Wright’s and Hale’s project of founding mathematics on abstraction principles (Hale & Wright, 2001; Cook, 2007). In Walsh (2012), it was noted that one traditional abstraction principle, namely Hume’s Principle, had a certain relative categoricity property, which here we term natural relative categoricity. In this paper, we show that most other abstraction principles are not naturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. To better understand the precise demands of relative categoricity in the context of abstraction principles, we compare and contrast these constraints to (i) stability-like acceptability criteria on abstraction principles (cf. Cook, 2012), (ii) the Tarski-Sher logicality requirements on abstraction principles studied by Antonelli (2010b) and Fine (2002), and (iii) supervaluational ideas coming out of the work of Hodes (1984, 1990, 1991).

A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here, an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of representation from contemporary mathematical logic. It is argued that the theory-based versions of such logicism are either too liberal (the plethora problem) or are committed to intuitively incorrect closure conditions (the consistency problem). Structure-based versions must on the other hand respond to a charge of begging the question (the circularity problem) or explain how one may have a knowledge of structure in advance of a knowledge of axioms (the signature problem). This discussion is significant because it gives us a better idea of what a notion of representation must look like if it is to aid in realizing some of the traditional epistemic aims of logicism in the philosophy of mathematics.

The megalithic tombs of the Tramore group in County Waterford, south-eastern Ireland, are described and reconsidered. Three are confirmed as passage-tombs, but two are now identified as wedge-tombs. The passage-tombs have their best parallels not in Ireland, but in the Scilly Isles and Cornwall.

A persistent difficulty in terrestrial planet formation models is creating Mars analogs with the appropriate mass: Mars is typically an order of magnitude too large in simulations. Some recent work found that a small Mars can be created if the planetesimal disk from which the planets form has an outermost edge at 1.0 AU. However, that work and no previous work could produce a truncation of the planetesimal disk while also explaining the mass and structure of the asteroid belt. We show that gas-driven migration of Jupiter inward to 1.5 AU, before its subsequent outward migration, can truncate the disk and repopulate the asteroid belt. This dramatic migration history of Jupiter suggests that the dynamical behavior of our giant planets was more similar to that inferred for extra-solar planets than previously thought, as both have been characterised by substantial radial migration.

Once-extensive Eastern Oyster (Crassostrea virginica) reefs in the Hudson-Raritan Estuary (HRE) were destroyed almost a century ago as a result of human activities. However, because of improvements in water quality, the potential exists to reintroduce this ecologically extinct species to the ecosystem. For over a decade, New York/New Jersey Baykeeper has conducted oyster restoration activities in support of target ecological goals proposed in the HRE Comprehensive Restoration Plan (CRP). The critical research question is whether existing conditions at a proposed restoration site can actually support long-term Eastern Oyster survival. To determine the feasibility of restoring this native species in Keyport Harbor, New Jersey, juvenile oysters were placed in research field plots, and survivorship and growth were monitored. Data from the first reported oyster restoration research in the New Jersey (NJ) portion of the HRE indicate that oysters could indeed be reintroduced into the ecosystem. After 11 months in situ, research oyster survival rates as high as 60% were observed. Qualitative tissue observations indicated female oysters produced eggs that appeared normal and were ready for spawning. Biodiversity of species collected from the field plots was two- to threefold greater with adult research oysters present, suggesting that oysters increased the density and abundance of other marine species. Sediment deposition patterns indicated that the presence of oysters in support structures may reduce the degree of topographic relief caused by winter storm energies. The research ended abruptly on August 9, 2010, when New Jersey's Department of Environmental Protection rescinded the project permit because of concerns that research oysters were beginning to reach New Jersey's market size of 2.5 inches. Although initial data suggest that oysters can survive and reproduce in Raritan Bay and the potential exists to achieve oyster restoration goals included in the CRP, the project also highlights the current lack of agreement between shellfishery regulators and restoration practitioners with respect to oyster reintroduction in waters where shellfish harvesting is currently prohibited. Different shellfish management approaches are used in New England states (Massachusetts, Rhode Island, and Connecticut), where local control is an important management tool, and in Chesapeake Bay states (Maryland and Virginia), where federal involvement is relatively high. Situated between these two distinct shellfish-producing regions, New Jersey and New York have not supported aggressive reestablishment of historic Eastern Oyster populations in the HRE, and unlike adjacent states, have not developed long-term oyster aquaculture plans. The reluctance to support oyster restoration is due to concerns related to human health and ecological questions. Examples of best management practices currently employed in neighboring states offer potential solutions to address regulatory concerns and could form the basis for developing a productive long-term strategy to reestablish Eastern Oysters in the HRE.

Environmental Practice 14:110–129 (2012)