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2014 Uniform Density in Lindenbaum Algebras
V. Yu. Shavrukov, Albert Visser
Notre Dame J. Formal Logic 55(4): 569-582 (2014). DOI: 10.1215/00294527-2798754


In this paper we prove that the preordering of provable implication over any recursively enumerable theory T containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function F for . A recursive function F is a density function if it computes, for A and B with AB, an element C such that ACB. The function is extensional if it preserves T-provable equivalence. Secondly, we prove a general result that implies that, for extensions of elementary arithmetic, the ordering restricted to Σn-sentences is uniformly dense. In the last section we provide historical notes and background material.


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V. Yu. Shavrukov. Albert Visser. "Uniform Density in Lindenbaum Algebras." Notre Dame J. Formal Logic 55 (4) 569 - 582, 2014.


Published: 2014
First available in Project Euclid: 7 November 2014

zbMATH: 1339.03056
MathSciNet: MR3276413
Digital Object Identifier: 10.1215/00294527-2798754

Primary: 03F40
Secondary: 03D45, 03F30

Rights: Copyright © 2014 University of Notre Dame


Vol.55 • No. 4 • 2014
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