25 found
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  1.  29
    In Search of Ultimate-L the 19th Midrasha Mathematicae Lectures.W. Hugh Woodin - 2017 - Bulletin of Symbolic Logic 23 (1):1-109.
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  2.  34
    Suitable Extender Models I.W. Hugh Woodin - 2010 - Journal of Mathematical Logic 10 (1):101-339.
  3.  77
    Suitable Extender Models II: Beyond Ω-Huge.W. Hugh Woodin - 2011 - Journal of Mathematical Logic 11 (2):115-436.
  4.  15
    The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal.W. Hugh Woodin - 2002 - Bulletin of Symbolic Logic 8 (1):91-93.
  5. Strong Axioms of Infinity and the Debate About Realism.Kai Hauser & W. Hugh Woodin - 2014 - Journal of Philosophy 111 (8):397-419.
    One of the most distinctive and intriguing developments of modern set theory has been the realization that, despite widely divergent incentives for strengthening the standard axioms, there is essentially only one way of ascending the higher reaches of infinity. To the mathematical realist the unexpected convergence suggests that all these axiomatic extensions describe different aspects of the same underlying reality.
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  6.  51
    On the Consistency Strength of the Inner Model Hypothesis.Sy-David Friedman, Philip Welch & W. Hugh Woodin - 2008 - Journal of Symbolic Logic 73 (2):391 - 400.
  7.  60
    The Necessary Maximality Principle for C. C. C. Forcing is Equiconsistent with a Weakly Compact Cardinal.Joel D. Hamkins & W. Hugh Woodin - 2005 - Mathematical Logic Quarterly 51 (5):493-498.
    The Necessary Maximality Principle for c. c. c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal.
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  8. $\Underset{\Tilde}{\Delta}^1_n$ Sets of Reals.Joan Bagaria & W. Hugh Woodin - 1997 - Journal of Symbolic Logic 62 (4):1379-1428.
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  9.  23
    Definability in the Enumeration Degrees.Theodore A. Slaman & W. Hugh Woodin - 1997 - Archive for Mathematical Logic 36 (4-5):255-267.
  10.  43
    The Cardinals Below|[Ω1]< Ω1|.W. Hugh Woodin - 2006 - Annals of Pure and Applied Logic 140 (1-3):161-232.
    The results of this paper concern the effective cardinal structure of the subsets of [ω1]<ω1, the set of all countable subsets of ω1. The main results include dichotomy theorems and theorems which show that the effective cardinal structure is complicated.
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  11. Infinity: New Research Frontiers.Rudy Rucker, Wolfgang Achtner, Enrico Bombieri, Edward Nelson, W. Hugh Woodin & Harvey M. Friedman - 2011 - Cambridge University Press.
    This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity.The book starts with a historical examination of the transformation of (...)
     
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  12.  48
    Incompatible Ω-Complete Theories.Peter Koellner & W. Hugh Woodin - 2009 - Journal of Symbolic Logic 74 (4):1155 - 1170.
    In 1985 the second author showed that if there is a proper class of measurable Woodin cardinals and $V^{B1} $ and $V^{B2} $ are generic extensions of V satisfying CH then $V^{B1} $ and $V^{B2} $ agree on all $\Sigma _1^2 $ -statements. In terms of the strong logic Ω-logic this can be reformulated by saying that under the above large cardinal assumption ZFC + CH is Ω-complete for $\Sigma _1^2 $ Moreover. CH is the unique $\Sigma _1^2 $ -statement (...)
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  13.  29
    The Transfinite Universe.W. Hugh Woodin - 2011 - In Matthias Baaz (ed.), Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press. pp. 449.
  14.  24
    Complexity of Reals in Inner Models of Set Theory.Boban Velickovic & W. Hugh Woodin - 1998 - Annals of Pure and Applied Logic 92 (3):283-295.
    We consider the possible complexity of the set of reals belonging to an inner model M of set theory. We show that if this set is analytic then either 1M is countable or else all reals are in M. We also show that if an inner model contains a superperfect set of reals as a subset then it contains all reals. On the other hand, it is possible to have an inner model M whose reals are an uncountable Fσ set (...)
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  15.  25
    The Realm of the Infinite.W. Hugh Woodin - 2011 - In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press. pp. 89.
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  16.  15
    Sets of Reals.Joan Bagaria & W. Hugh Woodin - 1997 - Journal of Symbolic Logic 62 (4):1379-1428.
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  17.  60
    Extending Partial Orders to Dense Linear Orders.Theodore A. Slaman & W. Hugh Woodin - 1998 - Annals of Pure and Applied Logic 94 (1-3):253-261.
    J. Łoś raised the following question: Under what conditions can a countable partially ordered set be extended to a dense linear order merely by adding instances of comparability ? We show that having such an extension is a Σ 1 l -complete property and so there is no Borel answer to Łoś's question. Additionally, we show that there is a natural Π 1 l -norm on the partial orders which cannot be so extended and calculate some natural ranks in that (...)
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  18.  43
    The Universe Constructed From a Sequence of Ordinals.W. Hugh Woodin - 1996 - Archive for Mathematical Logic 35 (5-6):371-383.
    We prove that if $V = L [s]$ where $s$ is an $\omega$ -sequence of ordinals then the GCH holds.
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  19.  26
    The Weak Ultrafilter Axiom.W. Hugh Woodin - 2016 - Archive for Mathematical Logic 55 (1-2):319-351.
  20.  31
    Sets and Singletons.Kai Hauser & W. Hugh Woodin - 1999 - Journal of Symbolic Logic 64 (2):590-616.
    We extend work of H. Friedman, L. Harrington and P. Welch to the third level of the projective hierarchy. Our main theorems say that (under appropriate background assumptions) the possibility to select definable elements of non-empty sets of reals at the third level of the projective hierarchy is equivalent to the disjunction of determinacy of games at the second level of the projective hierarchy and the existence of a core model (corresponding to this fragment of determinacy) which must then contain (...)
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  21.  31
    A Potential Subtlety Concerning the Distinction Between Determinism and Nondeterminism.W. Hugh Woodin - 2011 - In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press. pp. 119.
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  22.  15
    Atlanta Marriott Marquis, Atlanta, Georgia January 7–8, 2005.Matthias Aschenbrenner, Alexander Berenstein, Andres Caicedo, Joseph Mileti, Bjorn Poonen, W. Hugh Woodin & Akihiro Kanamori - 2005 - Bulletin of Symbolic Logic 11 (3).
  23.  11
    Super-Real Fields. Totally Ordered Fields with Additional Structure.H. Garth Dales & W. Hugh Woodin - 2000 - Bulletin of Symbolic Logic 6 (2):218-221.
  24.  6
    Ad and the Uniqueness of the Supercompact Measures on Pω 1.W. Hugh Woodin, A. S. Kechris, D. A. Martin, Y. N. Moschavokis & Alexander S. Kechris - 1992 - Journal of Symbolic Logic 57 (1):259-261.
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  25. 2002 Annual Meeting of the Association for Symbolic Logic.W. Hugh Woodin & Z. Beyond - 2003 - Bulletin of Symbolic Logic 9 (1):51.