On Weak Markov's Principle
Ulrich Kohlenbach December 2001 |

## Abstract:
We show that the so-called weak Markov's principle (WMP) which
states that every pseudo-positive real number is positive is underivable in
E-HAAC. Since
allows to
formalize (at least large parts of) Bishop's constructive mathematics this
makes it unlikely that WMP can be proved within the framework of Bishop-style
mathematics (which has been open for about 20 years). The underivability even
holds if the ineffective schema of full comprehension (in all types) for
negated formulas (in particular for -free formulas) is added which
allows to derive the law of excluded middle for such formulas.
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