Diener, Hannes; Hendtlass, Matthew

Completeness: When Enough is Enough

Doc. Math. 24, 899-914 (2019)
DOI: 10.25537/dm.2019v24.899-914


We investigate the notion of a complete enough metric space that, while classically vacuous, in a constructive setting allows for the generalisation of many theorems to a much wider class of spaces. In doing so, this notion also brings the known body of constructive results significantly closer to that of classical mathematics. Most prominently, we generalise the Kreisel-Lacome-Shoenfield Theorem/Tseytin's Theorem on the continuity of functions in recursive mathematics.

Mathematics Subject Classification

03F60, 03D78, 03F55


constructive mathematics, computable analysis, completeness


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Diener, Hannes
School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
Hendtlass, Matthew
School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand