SEPARATING MANY LOCALISATION CARDINALS ON THE GENERALISED BAIRE SPACE

Abstract Given a cofinal cardinal function $h\in {}^{\kappa }\kappa $ for $\kappa inaccessible, we consider the dominating h -localisation number, that is, least cardinality of set -slaloms such every -real is localised by slalom in set. It was proved [3] localisation numbers can be consistently different two functions (the identity and power function). We will construct ^+$ -sized family their corresponding numbers, use ${\leq -supported product cofinality-preserving forcing to prove any simultaneous assignment these cardinals above consistent. This answers an open question from [3].