Summable gaps Original Research Article

It is proved, under Martinʹs Axiom, that all (ω1,ω1) gaps in View the MathML source are indestructible in any forcing extension by a separable measure algebra. This naturally leads to a new type of gap, a summable gap. The results of these investigations have applications in Descriptive Set Theory. For example, it is shown that under Martinʹs Axiom the Baire categoricity of all Δ31 non-Δ31-complete sets of reals requires a weakly compact cardinal.