Category theory is often treated as an algebraic foundation for mathematics, and the widely known algebraization of ZF set theory in terms of this discipline is referenced as “categorical set theory” or “set theory for category theory”. The method of algebraization used in this theory has not been formulated in terms of universal algebra so far. In current paper, a _universal algebraic_ method, i.e. one formulated in terms of universal algebra, is presented and used for algebraization of a ground mereological (...) system described as “quantitative” (QMS) and of the standard set theories built upon it. The QMS is algebraized by using abelian generalized groups (AGGs) generalizing both abelian groups and Boolean algebras. To algebraize set theory, the AGG are enriched with operators to produce _extensional algebras_ (EA) of Tarskian “Boolean algebras with operators” type. EAs explicate the intuition of set theory’ universes (of discourse). The axiomatic set theory presented in this paper, named _extension theory_, previously went through an intuitive phase of development during its use by the author in computer science projects, where it served as the basis for development of a foundational data science framework and an extensional model of natural languages also outlined here. (shrink)

The European Legacy, Volume 17, Issue 5, Page 694-696, August 2012.

The aim of this paper is to evaluate the extent of the practice of using informal payments for accessing the services of public clinics or hospitals across Europe and to explain the prevalence of this corrupt practice using the framework of institutional theory. To achieve this, a multi-level mixed-effect logistic regression on 25,744 interviews undertaken in 2020 with patients across 27 European Union countries is conducted. The finding is that the practice of making informal payments remains a prevalent practice, although (...) there are large disparities in the usage of this practice in different European countries. However, informal payments by patients are more likely when there is a lower institutional trust and a higher degree of asymmetry between formal and informal institutions. The resultant proposal is that policy makers need to address the institutional environment to tackle such informal payments. How this can be achieved is outlined. (shrink)