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  1.  42
    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.  49
    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.  12
    Regularity Properties on the Generalized Reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
  4.  7
    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.  42
    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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  6.  10
    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.
    We study regularity properties related to Cohen, random, Laver, Miller and Sacks forcing, for sets of real numbers on the Δ31\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_3}$$\end{document} level of the projective hieararchy. For Δ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_2}$$\end{document} and Σ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Sigma}^1_2}$$\end{document} sets, the relationships between these properties follows the pattern of the well-known Cichoń diagram for cardinal characteristics of the continuum. It is known that (...)
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  7.  50
    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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