On the decidability of ℚªᵇ_p
I will propose an effective axiomatization for ℚªᵇ_p, the maximal abelian extension of the p-adics, and present a strategy for proving quantifier elimination (in a variant of the Macintyre language) for the theory thus axiomatized. This should eventually give the decidability of ℚªᵇ_p and all its finite extensions.