A class LT 0 of functions computable in a proper sub-class of Lintime is de ned, and formalized in a system LT0 of monadic and atomic (quanti er-free) logic. In spite of its poor computational complexity power and logical apparatus, this system has enough power to describe its own proof-predicate. Therefore it might qualify as smallest known system in which Godel-like diagonalization can be ap...

We study the representation theory of the superconformal algebra Wk(g, fθ) associated to a minimal gradation of g. Here, g is a simple finite-dimensional Lie superalgebra with a non-degenerate even supersymmetric invariant bilinear form. Thus, Wk(g, fθ) can be the Virasoro algebra, the Bershadsky-Polyakov algebra, the Neveu-Schwarz algebra, the BershadskyKnizhnik algebras, the N = 2 superconfor...

An MV-pair is a pair (B, G) where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain conditions. Let ∼G be the equivalence relation on B naturally associated with G. We prove that for every MV-pair (B, G), the effect algebra B/ ∼G is an MV-effect algebra. Moreover, for every MV-effect algebra M there is an MV-pair (B, G) such that M is isomorphic to B/ ∼G.

1 The Dialectica paper. In 1958, GG odel published in the journal Dialectica an interpretation of in-tuitionistic number theory in a quantiier-free theory of functionals of nite type; this subsequently came to be known as GG odel's functional or Dialectica interpretation. The article itself was written in German for an issue of that journal in honor of Paul Bernays' 70 th birthday. In 1965, Ber...

It is shown that Morita equivalence preserves quasi-Koszulity, and a finite-dimensional K-algebra A is quasi-Koszul if and only if the skew group algebra A * G is, where G is a finite group satisfying charK ∤ |G|. It follows from these results that a finite-dimensional K-algebra A is quasi-Koszul if and only if the smash product A#G * is, where G is a finite group satisfying charK ∤ |G|. Furthe...

Declarative meta-programming is vital, since it is the most promising means by which programs can be made to reason about other programs. A metaprogram is a program that takes another program, called the object program, as data. A declarative programming language is a programming language based on a logic that has a model theory. A meta-program operates on a representation of an object program....

The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra g sitting inside an associative algebra A and any associative algebra F we introduce and study the algebra (g,A)(F), which is the Lie subalgebra of F ⊗ A generated by F ⊗ g. In many examples A is the universal enveloping algebra of g. Our description of the algebra (g,A)(F)...