15 found
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  1.  37
    Mad Families, Splitting Families and Large Continuum.Jörg Brendle & Vera Fischer - 2011 - Journal of Symbolic Logic 76 (1):198 - 208.
    Let κ < λ be regular uncountable cardinals. Using a finite support iteration (in fact a matrix iteration) of ccc posets we obtain the consistency of b = a = κ < s = λ. If μ is a measurable cardinal and μ < κ < λ, then using similar techniques we obtain the consistency of b = κ < a = s = λ.
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  2.  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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  3.  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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  4.  13
    The Spectrum of Independence.Vera Fischer & Saharon Shelah - 2019 - Archive for Mathematical Logic 58 (7-8):877-884.
    We study the set of possible sizes of maximal independent families to which we refer as spectrum of independence and denote \\). Here mif abbreviates maximal independent family. We show that:1.whenever \ are finitely many regular uncountable cardinals, it is consistent that \\); 2.whenever \ has uncountable cofinality, it is consistent that \=\{\aleph _1,\kappa =\mathfrak {c}\}\). Assuming large cardinals, in addition to above, we can provide that $$\begin{aligned} \cap \hbox {Spec}=\emptyset \end{aligned}$$for each i, \.
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  5.  7
    Maximal Cofinitary Groups Revisited.Vera Fischer - 2015 - Mathematical Logic Quarterly 61 (4-5):367-379.
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  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.  41
    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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  8.  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.
    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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  9.  17
    Free Sequences in $${Mathscr {P}}Left /Text {Fin}$$ P Ω / Fin.David Chodounský, Vera Fischer & Jan Grebík - 2019 - Archive for Mathematical Logic 58 (7-8):1035-1051.
    We investigate maximal free sequences in the Boolean algebra \ {/}\text {fin}\), as defined by Monk :593–610, 2011). We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted \. Answering a question of Monk, we demonstrate the consistency of \. In fact, this consistency is demonstrated in the model of Shelah for \ :433–443, 1992). Our paper provides a streamlined (...)
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  10.  11
    Free sequences in $${\mathscr {P}}\left( \omega \right) /\text {fin}$$.David Chodounský, Vera Fischer & Jan Grebík - 2019 - Archive for Mathematical Logic 58 (7):1035-1051.
    We investigate maximal free sequences in the Boolean algebra \ {/}\text {fin}\), as defined by Monk :593–610, 2011). We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted \. Answering a question of Monk, we demonstrate the consistency of \. In fact, this consistency is demonstrated in the model of Shelah for \ :433–443, 1992). Our paper provides a streamlined (...)
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  11.  12
    Ideals of Independence.Vera Fischer & Diana Carolina Montoya - 2019 - Archive for Mathematical Logic 58 (5-6):767-785.
    We study two ideals which are naturally associated to independent families. The first of them, denoted \, is characterized by a diagonalization property which allows along a cofinal sequence of stages along a finite support iteration to adjoin a maximal independent family. The second ideal, denoted \\), originates in Shelah’s proof of \ in Shelah, 433–443, 1992). We show that for every independent family \, \\subseteq \mathcal {J}_\mathcal {A}\) and define a class of maximal independent families, to which we refer (...)
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  12.  4
    Free sequences in $${mathscr {P}}left /text {fin}$$ P ω / fin.David Chodounský, Vera Fischer & Jan Grebík - 2019 - Archive for Mathematical Logic 58 (7):1035-1051.
    We investigate maximal free sequences in the Boolean algebra \ {/}\text {fin}\), as defined by Monk :593–610, 2011). We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted \. Answering a question of Monk, we demonstrate the consistency of \. In fact, this consistency is demonstrated in the model of Shelah for \ :433–443, 1992). Our paper provides a streamlined (...)
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  13.  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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  14.  9
    A Co-Analytic Cohen-Indestructible Maximal Cofinitary Group.Vera Fischer, David Schrittesser & Asger Törnquist - 2017 - Journal of Symbolic Logic 82 (2):629-647.
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  15.  8
    A Co-Analytic Maximal Set of Orthogonal Measures.Vera Fischer & Asger Törnquist - 2010 - Journal of Symbolic Logic 75 (4):1403-1414.
    We prove that if V = L then there is a $\Pi _{1}^{1}$ maximal orthogonal (i.e., mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.
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