Two conjectures regarding the stability of ω-categorical theories
A. Lachlan (1974)
Fundamenta Mathematicae
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A. Lachlan (1974)
Fundamenta Mathematicae
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A. Lachlan (1980)
Fundamenta Mathematicae
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Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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Gerald Sacks (1979)
Fundamenta Mathematicae
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Yong Ge Tian, George P. H. Styan (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.
Bernard Aupetit, H. Mouton (1996)
Studia Mathematica
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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.
Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (2006)
Commentationes Mathematicae Universitatis Carolinae
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Several topological properties lying between the submetrizability and the -diagonal property are studied. We are mostly interested in their relationship to each other and to the submetrizability. The first example of a Tychonoff space with a regular -diagonal but without a zero-set diagonal is given. The same example shows that a Tychonoff separable space with a regular -diagonal need not be submetrizable. We give a necessary and sufficient condition for submetrizability of a regular...