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A local-global principle for the real continuum

Olivier Rioul 1, 2 José Carlos Magossi 3 
1 COMNUM - Communications Numériques
LTCI - Laboratoire Traitement et Communication de l'Information
2 COMELEC - Département Communications & Electronique
3 IC - Institute of Computing [Campinas]
Abstract : We discuss the implications of a local-global (or global-limit) principle for proving the basic theorems of real analysis. The aim is to improve the set of available tools in real analysis, where the local-global principle is used as a unifying principle from which the other completeness axioms and several classical theorems are proved in a fairly direct way. As a consequence, the study of the local-global concept can help establish better pedagogical approaches for teaching classical analysis.
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https://hal.telecom-paris.fr/hal-02300760
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Olivier Rioul, José Carlos Magossi. A local-global principle for the real continuum. Walter Carnielli; Jacek Malinowski. Contradictions, from Consistency to Inconsistency, 47, Springer, pp.213-240, 2018, Trends in Logic, 978-3-030-07534-7. ⟨10.1007/978-3-319-98797-2_11⟩. ⟨hal-02300760⟩

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