An interpolation theorem holds for many standard modal logics, but first order S5 is a prominent example of a logic for which it fails. In this paper it is shown that a first orde...
Directional Newton methods for functions f of n variables are shown to converge, under standard assumptions, to a solution of f(x) = 0. The rate of convergence is quadratic, for ne...
In any nonstandard model of Peano arithmetic, the standard part is not first order definable. But we show that in some model the standard part is definable as the unique solution ...
Let R be the preorder of embeddability between countable linear orders colored with elements of Rado’s partial order (a standard example of a wqo which is not a bqo). We show tha...
A new algorithm for building decision tree classifiers is proposed. The algorithm is executed in a distributed environment and is especially designed for classifying large datase...