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Ineffable limits of weakly compact cardinals and similar results
Límites inefables de cardinales débilmente compactos
DOI:
https://doi.org/10.15446/recolma.v54n2.93846Keywords:
Weakly compact cardinal, subtle cardinal, ineffable cardinal, ineffable set, Jónsson cardinal, Rowbottom cardinal, Ramsey cardinal (en)Cardinal débilmente compacto, cardinal sutil, cardinal inefable, conjunto inefable, cardinal Jónsson, cardinal Rowbottom, cardinal Ramsey (es)
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It is proved that if an uncountable cardinal κ has an ineffable subset of weakly compact cardinals, then κ is a weakly compact cardinal, and if κ has an ineffable subset of Ramsey (Rowbottom, Jónsson, ineffable or subtle) cardinals, then κ is a Ramsey (Rowbottom, J\'onsson, ineffable or subtle) cardinal.
Se prueba que si un cardinal no contable κ tiene un subconjunto casi inefable de cardinales débilmente compactos entonces κ es un cardinal débilmente compacto. Y si κ tiene un conjunto inefable de cardinales de Ramsey (Rowbottom, J\'onsson, inefables o sutiles) entonces κ es cardinal de Ramsey (Rowbottom, Jónsson, inefable o sutil).
References
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