A universal coefficient theorem in the setting of Kirchberg’s ideal-related KK -theory was obtained in the fundamental case of a Calgebra with one specified ideal by Bonkat in [1] and proved there to split, unnaturally, under certain conditions. Employing certain K-theoretical information derivable from the given operator algebras in a way introduced here, we shall demonstrate that Bonkat’s UCT...

We present a general framework for balancing expressions (terms) in form of so called tree straight-line programs. The latter can be seen as circuits over the free term algebra extended by contexts (terms with a hole) and the operations which insert terms/contexts into contexts. It is shown that for every term one can compute in DLOGTIME-uniform TC$^0$ a tree straight-line program of logarithmi...

We present some model theoretic results for {L}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by Chang and Keisler.We prove compactness theorem with respect to the class of allstructures taking values in the {L}ukasiewicz $texttt{BL}$-algebra.We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemizatio...

According to the Algorithmic Coding Theorem, minimal programs of any universal machine are prefix-codes asymptotically optimal with respect to the machine algorithmic probabilities. A stronger version of this result will be proven for a class of machines, not necessarily universal, and any semi-distribution. Furthermore, minimal programs with respect to universal machines will be shown to be al...

Teichmüller was the first person to point out explicitly the connection between quadratic differentials and the solutions of certain extremal problems in Function Theory. He enunciated the principle that if a point is required to be fixed the quadratic differential will have a simple pole there, if in addition fixed values are required for the first n derivatives of competing functions the quad...

Many verification approaches use SMT solvers in some form, and are limited by their incomplete handling of quantified formulas. Local reasoning allows to handle SMT problems involving a certain class of universally quantified formulas in a complete way by instantiation to a finite set of ground formulas. We present a method to generate these instances incrementally, in order to provide a more e...

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...