Classical W -algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel’fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension. These W -algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless KP-hierarchy). Th...

We strengthen a theorem of Gitik and Shelah [6] by showing that if κ is either weakly inaccessible or the successor of a singular cardinal and S is a stationary subset of κ such that NSκ S is saturated then κ \S is fat. Using this theorem we derive some results about the existence of fat stationary sets. We then strengthen some results due to Baumgartner and Taylor [2], showing in particular th...