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• W2938315078 abstract "We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first 'local-to-global' principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms are necessary to prove Pincherle's theorem, does not have an unique or unambiguous answer, in contrast to compactness. We establish similar differences for the computational properties of compactness and Pincherle's theorem. We establish the same differences for other local-to-global principles, even going back to Weierstrass. We also greatly sharpen the known computational power of compactness, for the most shared with Pincherle's theorem however. Finally, countable choice plays an important role in the previous, we therefore study this axiom together with the intimately related Lindelof lemma." @default.
• W2938315078 created "2019-04-25" @default.
• W2938315078 creator A5007539743 @default.
• W2938315078 creator A5073669576 @default.
• W2938315078 date "2018-08-29" @default.
• W2938315078 modified "2023-10-18" @default.
• W2938315078 title "Pincherle's theorem in Reverse Mathematics and computability theory" @default.
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• W2938315078 doi "https://doi.org/10.48550/arxiv.1808.09783" @default.
• W2938315078 hasPublicationYear "2018" @default.
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