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The situation of the intermediate value theorem is typical of many in constructive analysis, where we find one classical theorem with several constructive versions, some or all of which may be equivalent under classical logic. (See also, for example, Bridges et al. 1982.) There is one omniscience principle whose constructive status is less clear than that of LPO and LLPO—namely, Markov's principle (MP): For each binary sequence (an), if it is contradictory that all the terms an equal 0, then there exists a term equal to 1.
Pages: 175
Publisher: Springer; 2010 edition (May 18, 2010)
ISBN: 3642129390
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