Partition calculus and cardinal invariants

作者：Garti Shimon^*; Shelah Saharon

来源：Journal of the Mathematical Society of Japan, 2014, 66(2): 425-434.

DOI：10.2969/jmsj/06620425

• partition calculus
• cardinal characteristics

We prove that the strong polarized relation ((theta)(omega)) -> ((theta)(omega))(2)(1,1), applied simultaneously for every theta is an element of [Nu(1), 2(N0))], is consistent with ZFC. Consequently, , ((inv)(omega)) -> ((inv)(omega))(2)(1,1) is consistent for every cardinal invariant of the continuum. Some results in this direction are generalized to higher cardinals.
Nous prouvons que la relation polarisee forte ((theta)(omega)) -> ((theta)(omega))(2)(1,1), appliquee simultanement a chaque cardinal theta is an element of [Nu(1), 2(N0))], est en accord avec ZFC. Par consequent, la relation ((inv)(omega)) -> ((inv)(omega))(2)(1,1) est en accord avec ZFC pour chaque caracteristique sur le continu. Nous etudions plusieurs generalisations pour certains cardinaux eleves.

• 出版日期2014-4