Strong Completeness of Provability Logic for Uncountable Languages

Mohammad Golshani, Grigorii Stepanov, Reihane Zoghifard

For an ordinal $\lambda >0$, we use the Erdős--Rado partition theorem to prove the failure of strong completeness of $\mathsf{GL}$ for modal languages of cardinality $(2^{|λ|+\aleph_0})^{…