Classifying Isomorphi Residue Classes

Methods of Class Field Theory to Separate Logics over Finite Residue Classes and Circuit Complexity

Separations among the first-order logic Res(0,+,×) of finite residue classes, its extensions with generalized quantifiers, and in the presence of a built-in order are shown in this article, using algebraic methods from class field theory. These methods include classification of spectra of sentences over finite residue classes as systems of congruences, and the study of their h-densities over th...

Classifying Isomorphic Residue Classes

We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using di erent proving techniques, which are implemented as strategies in a multi-strategy proof planner. We show how these techniques help to successfully derive proofs in our domain and ex...

Approximating the Maximum Isomorphi Agreement Subtree is

Residue Classes of Lagrangian Subbundles and Maslov Classes

For Lagrangian subbundles with singularities in symplectic vector bundles, explicit formulas of relation between their residue classes and Maslov classes outside singularities are obtained. Then a Lagrangian subbundle with singularity is constructed where all possible Maslov classes are nonzero but residue classes vanish for dimension > 2 . Moreover, a Lagrangian immersion with singularity is c...

ar X iv : q - a lg / 9 60 50 09 v 1 5 M ay 1 99 6 QUANTUM CLASSIFYING SPACES & UNIVERSAL QUANTUM CHARACTERISTIC CLASSES

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to definin...