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Sy D. Friedman [48]Sy David Friedman [7]
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  1.  41
    Projective Wellorders and Mad Families with Large Continuum.Vera Fischer, Sy David Friedman & Lyubomyr Zdomskyy - 2011 - Annals of Pure and Applied Logic 162 (11):853-862.
    We show that is consistent with the existence of a -definable wellorder of the reals and a -definable ω-mad subfamily of [ω]ω.
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  2.  47
    Cardinal Characteristics and Projective Wellorders.Vera Fischer & Sy David Friedman - 2010 - Annals of Pure and Applied Logic 161 (7):916-922.
    Using countable support iterations of S-proper posets, we show that the existence of a definable wellorder of the reals is consistent with each of the following: , and.
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  3.  40
    Donald A. Martin. The Largest Countable This, That, and the Other. Cabal Seminar 79–81, Proceedings, Caltech-UCLA Logic Seminar 1979–81, Edited by A. S. Kechris, D. A. Martin, and Y. N. Moschovakis, Lecture Notes in Mathematics, Vol. 1019, Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1983, Pp. 97–106. - Alexander S. Kechris, Donald A. Martin, and Robert M. Solovay. Introduction to Q-Theory. Cabal Seminar 79–81, Proceedings, Caltech-UCLA Logic Seminar 1979–81, Edited by A. S. Kechris, D. A. Martin, and Y. N. Moschovakis, Lecture Notes in Mathematics, Vol. 1019, Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1983, Pp. 199–282. - Steve Jackson. AD and the Projective Ordinals. Cabal Seminar 81–85, Proceedings, Caltech-UCLA Logic Seminar 1981–85, Edited by A. S. Kechris, D. A. Martin, and J. R. Steel, Lecture Notes in Mathematics, Vol. 1333, Springer-Verlag, Berlin, Heidelberg, New York, Etc., 1988, Pp. 117–220. [REVIEW]Sy D. Friedman - 1992 - Journal of Symbolic Logic 57 (1):262-264.
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  4.  6
    Collapsing the Cardinals of HOD.James Cummings, Sy David Friedman & Mohammad Golshani - 2015 - Journal of Mathematical Logic 15 (2):1550007.
    Assuming that GCH holds and [Formula: see text] is [Formula: see text]-supercompact, we construct a generic extension [Formula: see text] of [Formula: see text] in which [Formula: see text] remains strongly inaccessible and [Formula: see text] for every infinite cardinal [Formula: see text]. In particular the rank-initial segment [Formula: see text] is a model of ZFC in which [Formula: see text] for every infinite cardinal [Formula: see text].
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  5.  5
    Regularity Properties on the Generalized Reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
  6.  11
    Coherent Systems of Finite Support Iterations.Vera Fischer, Sy D. Friedman, Diego A. Mejía & Diana C. Montoya - 2018 - Journal of Symbolic Logic 83 (1):208-236.
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  7. The Genericity Conjecture.Sy D. Friedman - 1994 - Journal of Symbolic Logic 59 (2):606-614.
  8.  21
    Hans-Dieter Donder and Peter Koepke. On the Consistency Strength of ‘Accessible’ Jonsson Cardinals and of the Weak Chang Conjecture. Annals of Pure and Applied Logic, Vol. 25 , Pp. 233–261. - Peter Koepke. Some Applications of Short Core Models. Annals of Pure and Applied Logic, Vol. 37 , Pp. 179–204. [REVIEW]Sy D. Friedman - 1989 - Journal of Symbolic Logic 54 (4):1496-1497.
  9.  9
    Cichoń’s Diagram, Regularity Properties and $${\Varvec{\Delta}^1_3}$$ Δ 3 1 Sets of Reals.Vera Fischer, Sy David Friedman & Yurii Khomskii - 2014 - Archive for Mathematical Logic 53 (5-6):695-729.
  10.  33
    Cardinal Characteristics, Projective Wellorders and Large Continuum.Vera Fischer, Sy David Friedman & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (7-8):763-770.
    We extend the work of Fischer et al. [6] by presenting a method for controlling cardinal characteristics in the presence of a projective wellorder and 2ℵ0>ℵ2. This also answers a question of Harrington [9] by showing that the existence of a Δ31 wellorder of the reals is consistent with Martinʼs axiom and 2ℵ0=ℵ3.
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  11.  20
    An Elementary Approach to the Fine Structure of L.Sy D. Friedman & Peter Koepke - 1997 - Bulletin of Symbolic Logic 3 (4):453-468.
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  12.  20
    Cardinal-Preserving Extensions.Sy D. Friedman - 2003 - Journal of Symbolic Logic 68 (4):1163-1170.
    A classic result of Baumgartner-Harrington-Kleinberg [1] implies that assuming CH a stationary subset of ω1 has a CUB subset in a cardinal-perserving generic extension of V, via a forcing of cardinality ω1. Therefore, assuming that $\omega_2^L$ is countable: { $X \in L \mid X \subseteq \omega_1^L$ and X has a CUB subset in a cardinal -preserving extension of L} is constructible, as it equals the set of constructible subsets of $\omega_1^L$ which in L are stationary. Is there a similar such (...)
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  13.  26
    Jensen's Σ* Theory and the Combinatorial Content of V = L.Sy D. Friedman - 1994 - Journal of Symbolic Logic 59 (3):1096 - 1104.
  14.  25
    Genericity and Large Cardinals.Sy D. Friedman - 2005 - Journal of Mathematical Logic 5 (02):149-166.
    We lift Jensen's coding method into the context of Woodin cardinals. By a theorem of Woodin, any real which preserves a "strong witness" to Woodinness is set-generic. We show however that there are class-generic reals which are not set-generic but preserve Woodinness, using "weak witnesses".
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  15.  11
    Steel Forcing and Barwise Compactness.Sy D. Friedman - 1982 - Annals of Mathematical Logic 22 (1):31-46.
  16.  14
    Jensen's $Sigma^Ast$ Theory and the Combinatorial Content of $V = L$.Sy D. Friedman - 1994 - Journal of Symbolic Logic 59 (3):1096-1104.
  17.  6
    Minimal Coding.Sy D. Friedman - 1989 - Annals of Pure and Applied Logic 41 (3):233-297.
  18.  46
    Co-Analytic Mad Families and Definable Wellorders.Vera Fischer, Sy David Friedman & Yurii Khomskii - 2013 - Archive for Mathematical Logic 52 (7-8):809-822.
    We show that the existence of a ${\Pi^1_1}$ -definable mad family is consistent with the existence of a ${\Delta^{1}_{3}}$ -definable well-order of the reals and ${\mathfrak{b}=\mathfrak{c}=\aleph_3}$.
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  19.  38
    Coding Without Fine Structure.Sy D. Friedman - 1997 - Journal of Symbolic Logic 62 (3):808-815.
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  20.  33
    Some Recent Developments in Higher Recursion Theory.Sy D. Friedman - 1983 - Journal of Symbolic Logic 48 (3):629-642.
    In recent years higher recursion theory has experienced a deep interaction with other areas of logic, particularly set theory (fine structure, forcing, and combinatorics) and infinitary model theory. In this paper we wish to illustrate this interaction by surveying the progress that has been made in two areas: the global theory of the κ-degrees and the study of closure ordinals.
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  21.  42
    A Guide to "Coding the Universe" by Beller, Jensen, Welch.Sy D. Friedman - 1985 - Journal of Symbolic Logic 50 (4):1002-1019.
  22.  8
    Annals of Pure and Applied Logic.Sy D. Friedman - 2001 - Bulletin of Symbolic Logic 7 (4):538-539.
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  23.  13
    A Simpler Proof of Jensen's Coding Theorem.Sy D. Friedman - 1994 - Annals of Pure and Applied Logic 70 (1):1-16.
    Jensen's remarkable Coding Theorem asserts that the universe can be included in L[R] for some real R, via class forcing. The purpose of this article is to present a simpler proof of Jensen's theorem, obtained by implementing some changes first developed for the theory of Strong Coding. In particular, our proof avoids the split into cases, according to whether or not 0# exists in the ground model.
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  24.  4
    A Guide to “Strong Coding”.Sy D. Friedman - 1987 - Annals of Pure and Applied Logic 35 (1):99-122.
  25.  5
    $0\Sp \#$ and Inner Models. [REVIEW]Sy D. Friedman - 2002 - Journal of Symbolic Logic 67 (3):924-932.
  26.  17
    HC of an Admissible Set.Sy D. Friedman - 1979 - Journal of Symbolic Logic 44 (1):95-102.
    If A is an admissible set, let HC(A) = {x∣ x ∈ A and x is hereditarily countable in A}. Then HC(A) is admissible. Corollaries are drawn characterizing the "real parts" of admissible sets and the analytical consequences of admissible set theory.
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  27.  11
    Degree Theory on ℵω.C. T. Chong & Sy D. Friedman - 1983 - Annals of Pure and Applied Logic 24 (1):87-97.
  28.  22
    Generic Σ₃¹ Absoluteness.Sy D. Friedman - 2004 - Journal of Symbolic Logic 69 (1):73 - 80.
  29.  8
    Strong Coding.Sy D. Friedman - 1987 - Annals of Pure and Applied Logic 35 (3):1-98.
  30.  12
    Classification Theory and 0#.Sy D. Friedman, Tapani Hyttinen & Mika Rautila - 2003 - Journal of Symbolic Logic 68 (2):580-588.
    We characterize the classifiability of a countable first-order theory T in terms of the solvability of the potential-isomorphism problem for models of T.
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  31.  19
    Generic Saturation.Sy D. Friedman - 1998 - Journal of Symbolic Logic 63 (1):158-162.
  32.  36
    Universally Baire Sets and Definable Well-Orderings of the Reals.Sy D. Friedman & Ralf Schindler - 2003 - Journal of Symbolic Logic 68 (4):1065-1081.
    Let n ≥ 3 be an integer. We show that it is consistent (relative to the consistency of n - 2 strong cardinals) that every $\Sigma_n^1-set$ of reals is universally Baire yet there is a (lightface) projective well-ordering of the reals. The proof uses "David's trick" in the presence of inner models with strong cardinals.
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  33.  23
    Coding Over a Measurable Cardinal.Sy D. Friedman - 1989 - Journal of Symbolic Logic 54 (4):1145-1159.
  34.  16
    Review: James E. Baumgartner, On the Size of Closed Unbounded Sets. [REVIEW]Sy D. Friedman - 2001 - Bulletin of Symbolic Logic 7 (4):538-539.
  35.  20
    Annual Meeting of the Association for Symbolic Logic.Sy D. Friedman - 1993 - Journal of Symbolic Logic 58 (1):370-382.
  36.  14
    Xlth Latin American Symposium on Mathematical Logic Merida, Venezuela, 6-1 0 July, 1998.C. A. Di Prisco, C. E. Uzcategui, J. Bagaria, Sy D. Friedman, R. Bianconi, E. A. Cichon, E. Tahhan-Bittar, M. E. Coniglio, F. Miraglia & J. P. Di'az Varela - 2001 - Annals of Pure and Applied Logic 108 (1-3):79-101.
  37.  14
    Review: Hans-Dieter Donder, Peter Koepke, On the Consistency Strength of `Accessible' Jonsson Cardinals and of the Weak Chang Conjecture; Peter Koepke, Some Applications of Short Core Models. [REVIEW]Sy D. Friedman - 1989 - Journal of Symbolic Logic 54 (4):1496-1497.
  38.  11
    Review: Donald A. Martin, A. S. Kechris, D. A. Martin, Y. N. Moschovakis, The Largest Countable This, That, and the Other; Alexander S. Kechris, Donald A. Martin, Robert M. Solovay, Introduction to $Q$-Theory; Steve Jackson, A. S. Kechris, D. A. Martin, J. R. Steel, AD and the Projective Ordinals. [REVIEW]Sy D. Friedman - 1992 - Journal of Symbolic Logic 57 (1):262-264.
  39.  9
    Definability Degrees.Sy D. Friedman - 2005 - Mathematical Logic Quarterly 51 (5):448-449.
    We establish the equiconsistency of a simple statement in definability theory with the failure of the GCH at all infinite cardinals. The latter was shown by Foreman and Woodin to be consistent, relative to the existence of large cardinals.
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  40.  9
    < I> Δ_< Sub> 1-Definability.Sy D. Friedman & Boban Veličković - 1997 - Annals of Pure and Applied Logic 89 (1):93-99.
  41.  7
    Handbook of Mathematical Logic, Edited by Barwise Jon with the Cooperation of Keisler H. J., Kunen K., Moschovakis Y. N., and Troelstra A. S., Studies in Logic and the Foundations of Mathematics, Vol. 90, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1978 , Xi + 1165 Pp. [REVIEW]Sy D. Friedman - 1984 - Journal of Symbolic Logic 49 (3):975-980.
  42.  8
    Model Theory for L∞Ω1.Sy D. Friedman - 1984 - Annals of Pure and Applied Logic 26 (2):103-122.
  43.  1
    James E. Baumgartner. On the Size of Closed Unbounded Sets. Annals of Pure and Applied Logic, Vol. 54 , Pp. 195–227.Sy D. Friedman - 2001 - Bulletin of Symbolic Logic 7 (4):538-539.
  44.  6
    Beller A., Jensen R., and Welch P.. Coding the Universe. London Mathematical Society Lecture Note Series, No. 47. Cambridge University Press, Cambridge Etc. 1982, 353 Pp. [REVIEW]Sy D. Friedman - 1985 - Journal of Symbolic Logic 50 (4):1081-1081.
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  45.  9
    Review: A. Beller, R. Jensen, P. Welch, Coding the Universe. [REVIEW]Sy D. Friedman - 1985 - Journal of Symbolic Logic 50 (4):1081-1081.
  46.  7
    Δ1-Definability.Sy D. Friedman & Boban Veličković - 1997 - Annals of Pure and Applied Logic 89 (1):93-99.
    We isolate a condition on a class A of ordinals sufficient to Δ1-code it by a real in a class-generic extension of L. We then apply this condition to show that the class of ordinals of L-cofinality ω is Δ1 in a real of L-degree strictly below O#.
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  47.  4
    1996–97 Annual Meeting of the Association for Symbolic Logic.Sy D. Friedman - 1997 - Bulletin of Symbolic Logic 3 (3):378-396.
  48.  3
    Generic Σ3 1 Absoluteness.Sy D. Friedman - 2004 - Journal of Symbolic Logic 69 (1):73-80.
  49.  2
    Annual Meeting of the Association for Symbolic Logic, Durham, 1992.Sy D. Friedman - 1993 - Journal of Symbolic Logic 58 (1):370-382.
  50. Model Theory for< I> L_< Sub>∞ Ω1.Sy D. Friedman - 1984 - Annals of Pure and Applied Logic 26 (2):103-122.
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