2 N ov 2 00 8 Nonstandard Consequence Operators Generated By Mixed Logic - Systems

Nonstandard Consequence Operators Generated by Mixed Logic-systems

Mixed logic-systems contain both standard and nonstandard coordinate values. In this paper, it is shown that each of the specifically defined mixed logic-systems generates an internal nonstandard conse-

Nonstandard Consequence Operators

In 1963, Abraham Robinson applied his newly discovered nonstandard analysis to formal firstorder languages and developed a nonstandard logic [9] relative to the “truth” concept and structures. Since that time not a great deal of fundamental research has been attempted in this specific area with one notable exception [2]. However, when results from this discipline are utilized they have yielded ...

N ov 2 00 3 NONSTANDARD ANALYSIS - A SIMPLIFIED APPROACH -

1 7 N ov 2 00 6 Principal subspaces of higher - level standard ̂ sl ( 3 ) - modules

We use the theory of vertex operator algebras and intertwining operators to obtain systems of q-difference equations satisfied by the graded dimensions of the principal subspaces of certain level k standard modules for ŝl(3). As a consequence we establish new formulas for the graded dimensions of the principal subspaces corresponding to the highest weights iΛ1 + (k − i)Λ2, where 1 ≤ i ≤ k and Λ...

ar X iv : 0 81 1 . 22 73 v 2 [ m at h . FA ] 1 5 N ov 2 00 8 Products of Longitudinal Pseudodifferential Operators on Flag Varieties

Associated to each set S of simple roots for SL(n, C) is an equivariant fibration X → XS of the space X of complete flags of C n. To each such fi-bration we associate an algebra JS of operators on L 2 (X) which contains, in particular, the longitudinal pseudodifferential operators of negative order tangent to the fibres. These form a lattice of operator ideals whose common intersection is the c...