Ω-logic

In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin (1999) as part of an inquiry into non-specific large cardinal axioms and the determinacy of corresponding pointclasses, while involving a controversial argument that the continuum hypothesis is false.

Woodin's Ω-conjecture asserts that if there is a proper class of Woodin cardinals, then Ω-logic satisfies an analogue of the completeness theorem.

References

• Bagaria, Joan; Castells, Neus; Larson, Paul (2006), "An Ω-logic primer", Set theory, Trends Math., Basel, Boston, Berlin: Birkhäuser, pp. 1–28, ISBN 978-3-7643-7691-8, MR2267144, http://www.users.muohio.edu/larsonpb/omegalogicmaster5.pdf 
• Dehornoy, Patrick (2004), "Progrès récents sur l'hypothèse du continu (d'après Woodin)", Astérisque (294): 147–172, ISSN 0303-1179, MR2111643, http://www.math.unicaen.fr/~dehornoy/Surveys/Dgt.pdf 
• Woodin, W. Hugh (1999), The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, Walter de Gruyter, ISBN 311015708X, MR1713438, http://books.google.com/?id=bQ9pQwVt8CsC 
• Woodin, W. Hugh (2001), "The continuum hypothesis. I", Notices of the American Mathematical Society 48 (6): 567–576, ISSN 0002-9920, MR1834351, http://www.ams.org/notices/200106/fea-woodin.pdf 
• Woodin, W. Hugh (2001b), "The Continuum Hypothesis, Part II", Notices of the AMS 48 (7): 681–690, http://www.ams.org/notices/200107/fea-woodin.pdf 
• Woodin, W. Hugh (2005), "The continuum hypothesis", in Cori, Rene; Razborov, Alexander; Todorcevic, Stevo et al., Logic Colloquium 2000, Lect. Notes Log., 19, Urbana, IL: Assoc. Symbol. Logic, pp. 143–197, MR2143878, http://www.aslonline.org/books-lnl_19.html 

External links

• W. H. Woodin Slides for 3 talks