Ω-logic

In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin (1999) as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure ${\displaystyle H_{\aleph _{2}}}$. Just as the axiom of projective determinacy yields a canonical theory of ${\displaystyle H_{\aleph _{1}}}$, 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.