Geodesic
Compactness phenomena in HOD
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e118

Voir la notice de l'article provenant de la source Cambridge University Press

We prove two compactness theorems for HOD. First, if $\kappa $ is a strong limit singular cardinal with uncountable cofinality and for stationarily many $\delta <\kappa $, $(\delta ^+)^{\mathrm {HOD}}=\delta ^+$, then $(\kappa ^+)^{\mathrm {HOD}}=\kappa ^+$. Second, if $\kappa $ is a singular cardinal with uncountable cofinality and stationarily many $\delta <\kappa $ are singular in $\operatorname {\mathrm {HOD}}$, then $\kappa $ is singular in $\operatorname {\mathrm {HOD}}$. We also discuss the optimality of these results and show that the first theorem does not extend from $\operatorname {\mathrm {HOD}}$ to other $\omega $-club amenable inner models. 
Goldberg, Gabriel; Poveda, Alejandro. Compactness phenomena in HOD. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e118. doi: 10.1017/fms.2025.10070
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