The tree property at the double successor
of a measurable cardinal $\kappa $ with $2^{\kappa} $ large
Fundamenta Mathematicae, Tome 223 (2013) no. 1, pp. 55-64
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Assuming the existence of a $\lambda ^+$-hypermeasurable cardinal $\kappa $, where $\lambda $ is the first weakly compact cardinal above $\kappa $, we prove that, in some forcing extension, $\kappa $ is still measurable, $\kappa ^{++}$ has the tree property and $2^\kappa =\kappa ^{+++}$. If the assumption is strengthened to the existence of a $\theta $-hypermeasurable cardinal (for an arbitrary cardinal $\theta >\lambda $ of cofinality greater than $\kappa $) then the proof can be generalized to get $2^\kappa =\theta $.
Keywords:
assuming existence lambda hypermeasurable cardinal nbsp kappa where lambda first weakly compact cardinal above kappa prove forcing extension kappa still measurable kappa has tree property kappa kappa assumption strengthened existence theta hypermeasurable cardinal arbitrary cardinal theta lambda cofinality greater kappa proof generalized get kappa theta
Affiliations des auteurs :
Sy-David Friedman 1 ; Ajdin Halilović 2
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Sy-David Friedman; Ajdin Halilović. The tree property at the double successor
of a measurable cardinal $\kappa $ with $2^{\kappa} $ large. Fundamenta Mathematicae, Tome 223 (2013) no. 1, pp. 55-64. doi: 10.4064/fm223-1-4
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