Cost monadic logic extends monadic second-order logic with the ability to measure the cardinal of sets. In particular, it allows to decide problems related to boundedness questions. In this paper, we provide new decidability results allowing the systematic investigation of questions involving “relative boundedness”. The first contribution in this work is to introduce a suitable logic for such q...

We characterize those models of ZFC which are embeddable, as the class of all standard sets, in a model of internal set theory IST .

A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. One possibility is to find a scheme in which a unique set is selected in some way. However, in this paper we consider the alternative approach in which all consistent sets are kept, leading to a type of ‘many world-views’ picture of t...

Do infinitesimals exist? This question arises naturally in calculus when one wants to write f(x+Δx) f(x) + f ′(x)Δx. This equation should hold for infinitesimal Δx where the notation a b means that a− b is infinitesimal. Much calculus can be done without bothering to define infinitesimal and using the equation above as a working definition of f ′(x). For mathematicians, of course, this is not a...

The interaction of Magnesium hydrate at the phosphate oxygen atom of the pyrimidine nucleotides (CMP,UMP,dTMP) were studied at the Hartree-Fock level Theory. We used LANL2DZ basis set for Mg and 6-31g* basis set for atoms.The basis set superposition error (BSSE) begins to converge for used Method/basis set. The gauge-invariant atomic orbital (GIAO) method and the continuous-set-of-gauge-transfo...

The notion of vague ideals in pseudo MV-algebras is introduced,and several properties are investigated. Conditions for a vague set to be avague ideal are provided. Conditions for a vague ideal to be implicative aregiven. Characterizations of (implicative, prime) vague ideals are discussed.The smallest vague ideal containing a given vague set is established. Primeand implicative extension proper...