A complete axiomatization of infinitary first-order intuitionistic logic over ${\mathcal{L}}_{{\kappa }^{+},\kappa }$

Christian Espíndola

Given a weakly compact cardinal $\kappa$, we give an axiomatization of intuitionistic first-order logic over ${\mathcal{L}}_{{\kappa }^{+},\kappa }$ and prove it is sound and complete with respect to Kr…