In this paper we prove that the preordering of provable implication over any recursively enumerable theory containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function for . A recursive function is a density function if it computes, for and with , an element such that . The function is extensional if it preserves -provable equivalence. Secondly, we prove a general result that implies that, for extensions of elementary arithmetic, the ordering restricted to -sentences is uniformly dense. In the last section we provide historical notes and background material.
"Uniform Density in Lindenbaum Algebras." Notre Dame J. Formal Logic 55 (4) 569 - 582, 2014. https://doi.org/10.1215/00294527-2798754