29 found
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  1.  44
    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.  17
    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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  3.  53
    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.  48
    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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  5.  15
    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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  6.  13
    Free sequences in $${\mathscr {P}}\left( \omega \right) /\text {fin}$$.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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  7.  19
    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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  8.  11
    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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  9.  17
    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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  10.  11
    Maximal cofinitary groups revisited.Vera Fischer - 2015 - Mathematical Logic Quarterly 61 (4-5):367-379.
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  11.  4
    Projective well orders and coanalytic witnesses.Jeffrey Bergfalk, Vera Fischer & Corey Bacal Switzer - 2022 - Annals of Pure and Applied Logic 173 (8):103135.
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  12.  8
    The spectrum of independence, II.Vera Fischer & Saharon Shelah - 2022 - Annals of Pure and Applied Logic 173 (9):103161.
  13.  9
    Partition Forcing and Independent Families.Jorge A. Cruz-Chapital, Vera Fischer, Osvaldo Guzmán & Jaroslav Šupina - 2023 - Journal of Symbolic Logic 88 (4):1590-1612.
    We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$. In addition, we show that Shelah’s poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$.
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  14.  5
    Games on Base Matrices.Vera Fischer, Marlene Koelbing & Wolfgang Wohofsky - 2023 - Notre Dame Journal of Formal Logic 64 (2):247-251.
    We show that base matrices for P(ω)∕fin of regular height larger than h necessarily have maximal branches that are not cofinal. The same holds for base matrices of height h if tSpoiler
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  15.  13
    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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  16.  45
    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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  17.  12
    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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  18.  52
    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.  3
    Strongly unfoldable, splitting and bounding.Ömer Faruk Bağ & Vera Fischer - 2023 - Mathematical Logic Quarterly 69 (1):7-14.
    Assuming, we show that generalized eventually narrow sequences on a strongly inaccessible cardinal κ are preserved under a one step iteration of the Hechler forcing for adding a dominating κ‐real. Moreover, we show that if κ is strongly unfoldable, and λ is a regular cardinal such that, then there is a set generic extension in which.
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  20.  13
    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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  21.  5
    Cohen preservation and independence.Vera Fischer & Corey Bacal Switzer - 2023 - Annals of Pure and Applied Logic 174 (8):103291.
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  22.  6
    Correction to: Towers, mad families, and unboundedness.Vera Fischer, Marlene Koelbing & Wolfgang Wohofsky - 2023 - Archive for Mathematical Logic 62 (7):1159-1160.
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  23.  11
    Definable MAD families and forcing axioms.Vera Fischer, David Schrittesser & Thilo Weinert - 2021 - Annals of Pure and Applied Logic 172 (5):102909.
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  24.  5
    Fresh function spectra.Vera Fischer, Marlene Koelbing & Wolfgang Wohofsky - 2023 - Annals of Pure and Applied Logic 174 (9):103300.
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  25.  13
    Higher Independence.Vera Fischer & Diana Carolina Montoya - 2022 - Journal of Symbolic Logic 87 (4):1606-1630.
    We study higher analogues of the classical independence number on $\omega $. For $\kappa $ regular uncountable, we denote by $i(\kappa )$ the minimal size of a maximal $\kappa $ -independent family. We establish ZFC relations between $i(\kappa )$ and the standard higher analogues of some of the classical cardinal characteristics, e.g., $\mathfrak {r}(\kappa )\leq \mathfrak {i}(\kappa )$ and $\mathfrak {d}(\kappa )\leq \mathfrak {i}(\kappa )$. For $\kappa $ measurable, assuming that $2^{\kappa }=\kappa ^{+}$ we construct a maximal $\kappa $ -independent (...)
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  26.  3
    More zfc inequalities between cardinal invariants.Vera Fischer & Dániel T. Soukup - 2021 - Journal of Symbolic Logic 86 (3):897-912.
    Motivated by recent results and questions of Raghavan and Shelah, we present ZFC theorems on the bounding and various almost disjointness numbers, as well as on reaping and dominating families on uncountable, regular cardinals. We show that if $\kappa =\lambda ^+$ for some $\lambda \geq \omega $ and $\mathfrak {b}=\kappa ^+$ then $\mathfrak {a}_e=\mathfrak {a}_p=\kappa ^+$. If, additionally, $2^{<\lambda }=\lambda $ then $\mathfrak {a}_g=\kappa ^+$ as well. Furthermore, we prove a variety of new bounds for $\mathfrak {d}$ in terms of (...)
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  27.  1
    Tight Eventually Different Families.Vera Fischer & Corey Bacal Switzer - forthcoming - Journal of Symbolic Logic:1-26.
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  28.  3
    Towers, mad families, and unboundedness.Vera Fischer, Marlene Koelbing & Wolfgang Wohofsky - 2023 - Archive for Mathematical Logic 62 (5):811-830.
    We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are $${\mathcal {B}}$$ B -Canjar for any countably directed unbounded family $${\mathcal {B}}$$ B of the ground model. In particular, they preserve the unboundedness of any unbounded scale of the ground model. Moreover, we show that $${\mathfrak {b}}=\omega _1$$ b = ω 1 in every extension by the (...)
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  29.  5
    The structure of $$\kappa $$ -maximal cofinitary groups.Vera Fischer & Corey Bacal Switzer - 2023 - Archive for Mathematical Logic 62 (5):641-655.
    We study \(\kappa \) -maximal cofinitary groups for \(\kappa \) regular uncountable, \(\kappa = \kappa ^{. Revisiting earlier work of Kastermans and building upon a recently obtained higher analogue of Bell’s theorem, we show that: Any \(\kappa \) -maximal cofinitary group has \({ many orbits under the natural group action of \(S(\kappa )\) on \(\kappa \). If \(\mathfrak {p}(\kappa ) = 2^\kappa \) then any partition of \(\kappa \) into less than \(\kappa \) many sets can be realized as the (...)
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