Pincherle's theorem in reverse mathematics and computability theory

摘要: Abstract We study the logical and computational properties of basic theorems uncountable mathematics, in particular Pincherle's theorem, published 1882. This theorem states that a locally bounded function is on certain domains, i.e. one first ‘local-to-global’ principles. It well-known such principles analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness theorem. For instance, main question Reverse Mathematics, namely which set existence axioms necessary prove does not have an unique or unambiguous answer, contrast compactness. establish similar for same other local-to-global principles, even going back Weierstrass. also greatly sharpen known power most shared with however. Finally, countable choice plays important role previous, therefore this axiom together related Lindelof lemma.