---
tag: 44BNWFBZ1A
kind: concept
name: Ω-logic
aliases: [omega-conjecture, conjecture, provability, valid, validity]
sources:
  - wikipedia: en:13772472@r1336097018
    locator: Ω-logic
    note: adopted
    mention: wikipedia://en/13772472
    sections: [Summary]
same_as:
  wikidata: Q8084001
  wikipedia: Ω-logic
inventory: [63GZRHWXQA]
---

## 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|0MN2MER9WN]] is false.