On Weak Markov's Principle
نویسنده
چکیده
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 ω :=EHA+AC. Since T ω 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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عنوان ژورنال:
- Math. Log. Q.
دوره 48 شماره
صفحات -
تاریخ انتشار 2002