Separability, Boxicity, and Partial Orders

Filters and Partial Orders

We discuss several abstract semantics for nonmonotonic logics. We present their motivations, their development and some historical origins, and show that the three systems considered are essentially

Partial Orders on Partial Isometries

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spac...

Extending Partial Orders to Dense Linear Orders

Partial Orders and Euclidean Geometry

Reverse Mathematics and Partial Orders

We investigate the reverse mathematics of several theorems about partial orders. We mainly focus on the analysis of scattered (no copy of the rationals) and FAC (no infinite antichains) partial orders, for which we consider many characterization theorems (for instance the wellknown Hausdorff’s theorem for scattered linear orders). We settle the proof-theoretic strength of most of these theorems...