Completitud y continuidad en Fundamentos de la Geometría de Hilbert: acerca del Vollständigkeitsaxiom

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THEORIA. An International Journal for Theory, History and Foundations of Science, ISSN: 0495-4548, Vol: 28, Issue: 1, Page: 139-163

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Eduardo Nicolás Giovannini
UPV/EHU Press; Euskal Herriko Unibertsitatea / Universidad del País Vasco
Arts and Humanities
article description
The paper reports and analyzes the vicissitudes around Hilbert's inclusion of his famous axiom of completeness, into his axiomatic system for Euclidean geometry. This task is undertaken on the basis of his unpublished notes for lecture courses, corresponding to the period 1894-1905. It is argued that this historical and conceptual analysis not only sheds new light on how Hilbert conceived originally the nature of his geometrical axiom of completeness, but also it allows to clarify some misunderstandings regarding this axiom and the metalogical property of completeness of an axiomatic system, as it was understood by Hilbert in this initial stage.