In 1981, Paris and Wilkie [28] indicated it was an open question whether IΣ0 would satisfy the Second Incompleteness Theorem for Herbrand deduction. We will show that some specially formulated axiomizations for IΣ0 can evade the Herbrandized version of the Second Incompleteness Theorem.

Competitiveness of an organization in the marketplace depends to a large extend on the adeptness of the business process in efficiently managing the workflow of an entity. Challenges that face business processes today is the inability reconfigure themselves based on knowledge from the workflow. The paper presents a framework that will allow information from the workflow to be stored as ontology...

The aim of this paper is to examine the concentration of wealth among the group of top wealth holders, defined as those with wealth in excess of a high cut off. The paper begins by considering the definition of this cut off, analogous to the definition of a poverty line at the other end of the distribution. It then considers what can be learned about the proportion classified as ‘rich’ and abou...

We begin the development of a theory of Banach spaces in the definable setting of o-minimal structures. We outline several results which develop the theory of compact embeddings for explicitly given function spaces. One aim is to explain the substantive underpinnings of an important observation used in the proof of the Reparameterization Theorem of Pila and Wilkie in [2]. We place this observat...

Collaborative filtering is an important personalized method in recommender systems in E-commerce. It is infeasible that traditional collaborative filtering is based on absolute rating for items since users are difficult to accurately make an absolute rating for items, and also different users give different rating distribution. In this paper, an improved collaborative filtering algorithm based ...

The growing number of tools for data novices are not designed with the goal of learning in mind. This paper proposes a set of pedagogical design principles for tool development to support data literacy learners. We document their use in the creation of three digital tools and activities that help learners build data literacy, showing design decisions driven by our pedagogy. Sketches students cr...

BEA is studying proposals to change the treatment of insurance services in the national accounts. There are 5 proposed changes: investment income will be added as a supplement to the premiums paid by policyholders; investment income is to include interest, dividends and capital gains; a measure of expected investment income will be incorporated; a measure of expected claims will be incorporated...

Various alternatives are available when designing a data collection system for portfolio investment (PI) statistics, in the context of balance of payments (BOP) and international investment position (IIP). Such systems differ according to the reporting agents they target, periodicity and level of aggregation, while the corresponding results vary in terms of implementation and running costs, ava...

CONDENSED statements of Association finances for the year 1952, prepared by the auditing firm of G. P. Graham & Company, are published herewith, in order that the entire membership may be fully informed regarding the financial operations, obligations, and resources of the AAAS. The first two statements summarize operating receipts and expenditures. Once again the annuity payments to the Cattell...

We expose a theorem of Pila and Wilkie on counting rational points in sets definable in o-minimal structures and some applications of this theorem to problems in diophantine geometry due to Masser, Peterzil, Pila, Starchenko, and Zannier.