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arXiv · 2606.08863

Monotone convergence theorems equivalent to Markov's principle

Douglas S. Bridges
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Abstract

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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Douglas S. Bridges. 2026-06-07. Monotone convergence theorems equivalent to Markov's principle. https://arxiv.org/abs/2606.08863

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