Annals of Pure and Applied Logic 171 (5):102788 (2020)

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 Lindelöf lemma.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2020.102788
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 50,268
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Reverse Mathematics and the Coloring Number of Graphs.Matthew Jura - 2016 - Notre Dame Journal of Formal Logic 57 (1):27-44.
The Dirac Delta Function in Two Settings of Reverse Mathematics.Sam Sanders & Keita Yokoyama - 2012 - Archive for Mathematical Logic 51 (1-2):99-121.
Nonstandard Models in Recursion Theory and Reverse Mathematics.C. T. Chong, Wei Li & Yue Yang - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
Reverse-Engineering Reverse Mathematics.Sam Sanders - 2013 - Annals of Pure and Applied Logic 164 (5):528-541.
The Monotone Completeness Theorem in Constructive Reverse Mathematics.Takako Nemoto & Hajime Ishihara - 2019 - In Peter Schuster, Deniz Sarikaya, Sara Negri & Stefania Centrone (eds.), Mathesis Universalis, Computability and Proof. Springer Verlag.
Classifying Dini's Theorem.Josef Berger & Peter Schuster - 2006 - Notre Dame Journal of Formal Logic 47 (2):253-262.
Reverse Mathematics and Infinite Traceable Graphs.Peter Cholak, David Galvin & Reed Solomon - 2012 - Mathematical Logic Quarterly 58 (1-2):18-28.
The Modal Logic of Reverse Mathematics.Carl Mummert, Alaeddine Saadaoui & Sean Sovine - 2015 - Archive for Mathematical Logic 54 (3-4):425-437.
Partial Impredicativity in Reverse Mathematics.Henry Towsner - 2013 - Journal of Symbolic Logic 78 (2):459-488.


Added to PP index

Total views
9 ( #848,637 of 2,325,507 )

Recent downloads (6 months)
9 ( #74,764 of 2,325,507 )

How can I increase my downloads?


My notes