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Independencia del Problema de Whitehead para Algebristas
Independence of Whitehead's Problem for Algebraists
Keywords:
grupo libre, grupo de Whitehead, subgrupo puro, principios de diamante, axioma de Martin (es)free group, Whitehead group, pure subgroup, diamond principles, Martin's axiom (en)
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Basados en el trabajo de P. Eklof [4], ofrecemos una prueba completa de la independencia del Problema de Whitehead para grupos abelianos de cardinalidad arbitaria. Dicha demostración fue establecida originalmente por S. Shelah [16, 17] como consecuencia de su famoso Teorema de Compacidad para álgebras universales. Como parte de este trabajo proponemos, basados en [5], una prueba simplificada del Teorema de Compacidad de Shelah para grupos abelianos.
Supported on P. Eklof's work [4], we present a complete proof of the independence of Whitehead's Problem for abelian groups of arbitrary cardinality. Such proof was established by S. Shelah [16, 17] as a consequence of his famous Compactness Theorem for universal algebras. As a part of this paper we propose, based on [5], a simplified proof of Shelah's Compactness Theorem for abelian groups.
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