This paper presents empirical evidence for five hypotheses about learning from large noisy domains: that trees built from very large training sets are larger and more accurate than trees built from even large subsets; that this increased accuracy is only in part due to the extra size of the trees; and that the extra training instances allow both better choices of attribute while building the tr...

Utilizing the connection between uniform constantdepth circuits and first-order logic with numerical predicates, we are able to provide a purely logical characterization of uniformity based on the intrinsic properties of these predicates. By requiring a numerical predicate R to satisfy a natural extensibility condition — that it can be translated to a polynomially magnified domain based on tupl...

Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The precise relationship of the various definitions used in the two disciplines has so far been neglected, a situation this paper is meant to remedy. As the role of the Cauchy completion is relevant for both effective approa...