Ω-logic

Summary

In set theory, Ω-logic is an infinitary logic and deductive system proposed by (txt) as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure $H_{\aleph_2}$. Just as the axiom of projective determinacy yields a canonical theory of $H_{\aleph_1}$, he sought to find axioms that would give a canonical theory for the larger structure. The theory he developed involves a controversial argument that the continuum hypothesis is false.