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# Exhaustible sets in higher-type computation

@article{Escard2008ExhaustibleSI, title={Exhaustible sets in higher-type computation}, author={Mart{\'i}n H{\"o}tzel Escard{\'o}}, journal={Logical Methods in Computer Science}, year={2008}, volume={4} }

- Published 2008 in Logical Methods in Computer Science
DOI:10.2168/LMCS-4(3:3)2008

We say that a set is exhaustible if it admits algorithmic universal quantification for continuous predicates in finite time, and searchable if there is an algorithm that, given any continuous predicate, either selects an element for which the predicate holds or else tells there is no example. The Cantor space of infinite sequences of binary digits is known to be searchable. Searchable sets are exhaustible, and we show that the converse also holds for sets of hereditarily total elements in the… CONTINUE READING

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