On Weak Markov's Principle

Authors

  • Ulrich Kohlenbach

DOI:

https://doi.org/10.7146/brics.v8i51.21712

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 T^{omega}:= E-HA^{omega} + AC. Since T^{omega} 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 $\exists$-free formulas) is added which allows to derive the law of excluded middle for such formulas.

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Published

2001-12-04

How to Cite

Kohlenbach, U. (2001). On Weak Markov’s Principle. BRICS Report Series, 8(51). https://doi.org/10.7146/brics.v8i51.21712