Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Publicado
Independencia del Problema de Whitehead para Algebristas
Independence of Whitehead's Problem for Algebraists
Palabras clave:
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)
Descargas
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.
Referencias
Yushiro Aoki, Discontinuous homomorphisms on C(X) with the negation of CH and a weak forcing axiom, aceptado en Journal of the London Mathematical Society.
Keith J. Devlin, Constructibility, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1984.
Keith J. Devlin and Saharon Shelah, A weak version of which follows from 2X0 < 2X1 , Israel J. Math. 29 (1978), no. 2-3, 239-247.
Paul C. Eklof, Whitehead's problem is undecidable, Amer. Math. Monthly 83 (1976), no. 10, 775-788.
Paul C. Eklof, Shelah's singular compactness theorem, Publ. Mat. 52 (2008), no. 1, 3-18.
Laszlo Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970.
Laszlo Fuchs, Infinite abelian groups. Vol. II, Pure and Applied Mathematics. Vol. 36-II, Academic Press, New York-London, 1973.
Paul Hill, On the freeness of abelian groups: A generalization of Pontryagin's theorem, Bull. Amer. Math. Soc. 76 (1970), 1118-1120.
Peter John Hilton and Urs Stammbach, A course in homological algebra, Graduate Texts in Mathematics, Vol. 4, Springer-Verlag, New York-Berlin, 1971.
Ayako Itaba, Diego A. Mejía, and Teruyuki Yorioka, Some infinitely generated non-projective modules over path algebras and their extensions under Martin's axiom, J. Math. Soc. Japan 72 (2020), no. 2, 413-433.
Thomas Jech, Set theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003, The third millennium edition, revised and expanded.
Kenneth Kunen, Set theory: An introduction to independence proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam, 1983, Reprint of the 1980 original.
Diego A. Mejía, Independencia del Problema de Whitehead, Master's thesis, Universidad Nacional de Colombia, sede Medellín, 2008, p. 51.
L. Pontrjagin, The theory of topological commutative groups, Ann. of Math. (2) 35 (1934), no. 2, 361-388.
Joseph J. Rotman, An introduction to the theory of groups, third ed., Allyn and Bacon, Inc., Boston, MA, 1984.
Saharon Shelah, Infinite abelian groups, Whitehead problem and some constructions, Israel J. Math. 18 (1974), 243-256.
Saharon Shelah, A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals, Israel J. Math. 21 (1975), no. 4, 319-349.
R. M. Solovay and S. Tennenbaum, Iterated Cohen extensions and Souslin's problem, Ann. of Math. (2) 94 (1971), 201-245.
Karl Stein, Analytische Funktionen mehrerer komplexer Veränderlichen zu vorgegebenen Periodizitätsmoduln und das zweite Cousinsche Problem, Math. Ann. 123 (1951), 201-222.
