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arxiv: 2606.08863 · v1 · pith:3HWZGKWSnew · submitted 2026-06-07 · 🧮 math.LO

Monotone convergence theorems equivalent to Markov's principle

classification 🧮 math.LO
keywords convergenceprincipleapparentequivalentmarkovprovisionallyactuallyanti-specker
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The notions of provisional, negative, and apparent convergence to 0 are introduced. It is then shown that Markov's principle is equivalent, in Bishop-style constructive mathematics, to the statement `every decreasing sequence of real numbers provisionally convergent to 0 actually converges to 0', and that this equivalence holds with `provisionally' replaced by `negatively'. Finally, apparent convergence and convergence are related by means of the anti-Specker principle.

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