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W. Hugh Woodin [25]W. H. Woodin [9]
  1.  91
    Kai Hauser & W. Hugh Woodin (2014). Strong Axioms of Infinity and the Debate About Realism. 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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  2. Joan Bagaria & W. Hugh Woodin (1997). $\Underset{\Tilde}{\Delta}^1_n$ Sets of Reals. Journal of Symbolic Logic 62 (4):1379-1428.
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  3.  13
    W. Hugh Woodin (2010). Suitable Extender Models I. Journal of Mathematical Logic 10 (01n02):101-339.
  4.  30
    Theodore A. Slaman & W. Hugh Woodin (1998). Extending Partial Orders to Dense Linear Orders. 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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  5.  27
    Joel D. Hamkins & W. Hugh Woodin (2005). The Necessary Maximality Principle for Ccc Forcing is Equiconsistent with a Weakly Compact Cardinal. 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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  6.  50
    W. Hugh Woodin (2011). Suitable Extender Models II: Beyond Ω-Huge. Journal of Mathematical Logic 11 (02):115-436.
  7.  14
    W. Hugh Woodin (2011). The Transfinite Universe. In Matthias Baaz (ed.), Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press 449.
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  8.  5
    Theodore A. Slaman & W. Hugh Woodin (1997). Definability in the Enumeration Degrees. Archive for Mathematical Logic 36 (4-5):255-267.
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  9. W. Hugh Woodin (2002). The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal. Bulletin of Symbolic Logic 8 (1):91-93.
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  10.  7
    W. Hugh Woodin (2011). The Realm of the Infinite. In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press 89.
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  11.  72
    Michał Heller & W. H. Woodin (eds.) (2011). Infinity: New Research Frontiers. Cambridge University Press.
    Machine generated contents note: Introduction Rudy Rucker; Part I. Perspectives on Infinity from History: 1. Infinity as a transformative concept in science and theology Wolfgang Achtner; Part II. Perspectives on Infinity from Mathematics: 2. The mathematical infinity Enrico Bombieri; 3. Warning signs of a possible collapse of contemporary mathematics Edward Nelson; Part III. Technical Perspectives on Infinity from Advanced Mathematics: 4. The realm of the infinite W. Hugh Woodin; 5. A potential subtlety concerning the distinction between determinism and nondeterminism W. (...)
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  12. Rudy Rucker, Wolfgang Achtner, Enrico Bombieri, Edward Nelson, W. Hugh Woodin & Harvey M. Friedman (2011). Infinity: New Research Frontiers. 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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  13.  2
    W. Hugh Woodin (2016). The Weak Ultrafilter Axiom. Archive for Mathematical Logic 55 (1-2):319-351.
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  14.  13
    W. Hugh Woodin (2006). The Cardinals Below|[Ω1]< Ω1|. 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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  15.  17
    Sy-David Friedman, Philip Welch & W. Hugh Woodin (2008). On the Consistency Strength of the Inner Model Hypothesis. Journal of Symbolic Logic 73 (2):391 - 400.
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  16.  12
    Peter Koellner & W. Hugh Woodin (2009). Incompatible Ω-Complete Theories. 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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  17.  12
    W. Hugh Woodin (2011). A Potential Subtlety Concerning the Distinction Between Determinism and Nondeterminism. In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press 119.
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  18.  2
    A. S. Kechris & W. H. Woodin (1991). A Strong Boundedness Theorem for Dilators. Annals of Pure and Applied Logic 52 (1-2):93-97.
    We prove a strong boundedness theorem for dilators: if A ⊆ DIL is Σ 1 1 , then there is a recursive dilator D 0 such that ∀ D ∈ A.
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  19.  5
    Boban Velickovic & W. Hugh Woodin (1998). Complexity of Reals in Inner Models of Set Theory. 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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  20.  6
    W. Hugh Woodin (1996). The Universe Constructed From a Sequence of Ordinals. 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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  21.  9
    E. Schimmerling & W. H. Woodin (2001). The Jensen Covering Property. Journal of Symbolic Logic 66 (4):1505-1523.
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  22.  5
    Kai Hauser & W. Hugh Woodin (1999). Sets and Singletons. Journal of Symbolic Logic 64 (2):590-616.
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  23.  16
    Kai Hauser & W. Hugh Woodin (1999). Π13 Sets and Π13 Singletons. 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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  24. Haim Judah, Saharon Shelah & W. H. Woodin (1990). The Borel Conjecture. Annals of Pure and Applied Logic 50 (3):255-269.
    We show the Borel Conjecture is consistent with the continuum large.
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  25.  3
    Kai Hauser & W. Hugh Woodin (1999). $Pi^13$ Sets and $Pi^13$ Singletons. 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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  26.  3
    W. H. Woodin (2006). The Cardinals Below Vertical Bar [Omega (1)]. Annals of Pure and Applied Logic 140 (1-3):161-232.
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  27.  2
    John Baldwin, Johanna Ny Franklin, C. Ward Henson, Julia F. Knight, Roman Kossak, Dima Sinapova, W. Hugh Woodin & Philip Scowcroft (2013). John B. Hynes Veterans Memorial Convention Center Boston Marriott Hotel, and Boston Sheraton Hotel Boston, MA January 6–7, 2012. [REVIEW] Bulletin of Symbolic Logic 19 (2).
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  28. J. Bagaria & W. H. Woodin (1997). 1\ Sets of Reals. Journal of Symbolic Logic 62 (4):1379-1428.
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  29.  1
    H. Garth Dales & W. Hugh Woodin (2000). Super-Real Fields. Totally Ordered Fields with Additional Structure. Bulletin of Symbolic Logic 6 (2):218-221.
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  30.  1
    Matthias Aschenbrenner, Alexander Berenstein, Andres Caicedo, Joseph Mileti, Bjorn Poonen, W. Hugh Woodin & Akihiro Kanamori (2005). Atlanta Marriott Marquis, Atlanta, Georgia January 7–8, 2005. Bulletin of Symbolic Logic 11 (3).
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  31. H. G. Dales & W. H. Woodin (1990). An Introduction to Independence for Analysts. Journal of Symbolic Logic 55 (1):361-362.
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  32.  1
    Q. Feng & W. H. Woodin (2003). P-Points in Qmax Models. Annals of Pure and Applied Logic 119 (1-3):121-190.
    We show how to get canonical models from in which the nonstationary ideal on ω1 is ω1 dense and there is no P-point.
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  33. S. Jackson, R. Ketchersid, F. Schlutzenberg & W. H. Woodin (2014). Determinacy and Jónsson Cardinals in L. Journal of Symbolic Logic 79 (4):1184-1198.
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  34. W. Hugh Woodin & Z. Beyond (2003). 2002 Annual Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 9 (1):51.
     
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