Provably total recursive functions and MRDP theorem in Basic Arithmetic and its extensions

We study Basic Arithmetic, BA introduced by W. Ruitenburg. BA is an arithmetical theory based on basic logic which is weaker than intuitionistic logic. We show that the class of the provably recursive functions of BA is a proper sub-class of primitive recursive functions. Three extensions of BA, called BA+U, BA_c and EBA are investigated with relation to their provably recursive functions. It is shown that the provably recursive functions of these three extensions of BA are exactly primitive recursive functions. Moreover, among other things, it is shown that the well-known MRDP theorem doesn't hold in BA, BA+U, BA_c, but holds in EBA

Interpolation Property on Visser's Formal Propositional Logic

 In this paper by using a model-theoretic approach, we prove Craig interpolation property for Formal Propositional Logic, FPL, Basic propositional logic, BPL and the uniform left-interpolation property for FPL. We also show that there are countably infinite extensions of FPL with the uniform interpolation property

Kindergarten in Kuwait

This research is concerned with the development of kindergarten education in Kuwait, especially with the modernisation of its curriculum which has been undertaken with the aim of making it more suitable, easier and convenient for teachers to use and more enjoyable and comprehensible for children, thus aiding their development. Consequently, this study seeks to identify problems currently facing preschools and to suggest solutions. To determine an appropriate solution, two strategies have formulated for tackling the problems. First, a structure questionnaire was drawn up and distributed to each of the sample of 84 teachers. Next, a case study was made of two kindergarten schools, one in an old city inhabited mostly by rich parents, and the other in a new city inhabited mainly by poor and polygamous parents. The intention was to cross-check the questionnaire results with those of the case study. This was placed in the context of a close examination of the development and operation of preschools in some Arabic countries. From the research, it was found that although the Kuwaiti kindergarten system of education is not inferior compared to those of other Arab countries, its continued progress is handicapped by a number of factors. Among these factors are an inadequate curriculum, lack of essential educational materials, lack of trained and or qualified teachers and overcrowded classrooms. As a result, it is recommended that the government should equip the Kuwaiti teaching institutes to prepare teachers for a professional career in kindergarten schools; employs more trained teachers and modernises the old schools to cope with overcrowding; motivates kindergarten teachers and finally redesigns the preschool curriculum so that it attains the highest standards and is flexible enough to enhance the creativity of the teachers and the knowledge of the children