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We analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of Lκ,κ. Using this equivalence we show that if any κ-complete filter on λ can be extended to a κ-complete ultrafilter and λ <κ = λ then (µ) fails for all regular µ ∈ [κ, 2 λ ]. As an application, we improve the lower bound for the consistency strength of κ-compactness, a case which was explicitly considered by Mitchell. 2010doi:10.4064/fm626-9-2018 fatcat:x3azwonlv5dwjpxy2w3kozavdm