David Pierce

Abraham Robinson's method for finding model completions is refined and and generalized for model companions and is applied to the theory of fields equipped with both a valuation and an automorphism.

This paper describes some of the results of a National Science Foundation Nanotechnology Undergraduate Education project that aims to establish a nanoscience and nanotechnology program at the University of North Dakota. The goal is to…

The theory of fields that are equipped with a countably infinite family of commuting derivations is not companionable; but if the axiom is added whereby the characteristic of the fields is zero, then the resulting theory is companionable.…

For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…

This paper grew out of the observation that the possibilities of proof by induction and definition by recursion are often confused. The paper reviews the distinctions. The von Neumann construction of the ordinal numbers includes a…

Finding simple, non-recursive, base noun phrases is an important subtask for many natural language processing applications. While previous empirical methods for base NP identification have been rather complex, this paper instead proposes a…