Results for 'Tree property'

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  1.  41
    Fragility and Indestructibility of the Tree Property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.
    We prove various theorems about the preservation and destruction of the tree property at ω 2. Working in a model of Mitchell [9] where the tree property holds at ω 2, we prove that ω 2 still has the tree property after ccc forcing of size ${\aleph_1}$ or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. (...)
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  2.  43
    The Tree Property and the Failure of SCH at Uncountable Cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.
    Given a regular cardinal λ and λ many supercompact cardinals, we describe a type of forcing such that in the generic extension there is a cardinal κ with cofinality λ, the Singular Cardinal Hypothesis at κ fails, and the tree property holds at κ +.
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  3.  18
    Finite Tree Property for First-Order Logic with Identity and Functions.Merrie Bergmann - 2005 - Notre Dame Journal of Formal Logic 46 (2):173-180.
    The typical rules for truth-trees for first-order logic without functions can fail to generate finite branches for formulas that have finite models–the rule set fails to have the finite tree property. In 1984 Boolos showed that a new rule set proposed by Burgess does have this property. In this paper we address a similar problem with the typical rule set for first-order logic with identity and functions, proposing a new rule set that does have the finite (...) property. (shrink)
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  4.  50
    A Remark on the Tree Property in a Choiceless Context.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (5-6):585-590.
    We show that the consistency of the theory “ZF + DC + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree property” follows from the consistency of a proper class of supercompact cardinals. This extends earlier results due to the author showing that the consistency of the theory “ ${{\rm ZF} + \neg{\rm AC}_\omega}$ + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal (...)
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  5.  11
    Theories Without the Tree Property of the Second Kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
    We initiate a systematic study of the class of theories without the tree property of the second kind — NTP2. Most importantly, we show: the burden is “sub-multiplicative” in arbitrary theories ; NTP2 is equivalent to the generalized Kimʼs lemma and to the boundedness of ist-weight; the dp-rank of a type in an arbitrary theory is witnessed by mutually indiscernible sequences of realizations of the type, after adding some parameters — so the dp-rank of a 1-type in any (...)
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  6.  19
    Notions Around Tree Property 1.Byunghan Kim & Hyeung-Joon Kim - 2011 - Annals of Pure and Applied Logic 162 (9):698-709.
    In this paper, we study the notions related to tree property 1 , or, equivalently, SOP2. Among others, we supply a type-counting criterion for TP1 and show the equivalence of TP1 and k- TP1. Then we introduce the notions of weak k- TP1 for k≥2, and also supply type-counting criteria for those. We do not know whether weak k- TP1 implies TP1, but at least we prove that each weak k- TP1 implies SOP1. Our generalization of the (...)-indiscernibility results in Džamonja and Shelah [5] is crucially used throughout the paper. (shrink)
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  7.  16
    The Tree Property and the Failure of the Singular Cardinal Hypothesis at ℵω2.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (3):934-946.
    We show that given ù many supercompact cardinals, there is a generic extension in which the tree property holds at ℵ ω²+1 and the SCH fails at ℵ ω².
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  8.  5
    The Tree Property at א Ω+2.Sy-David Friedman & Ajdin Halilović - 2011 - Journal of Symbolic Logic 76 (2):477 - 490.
    Assuming the existence of a weakly compact hypermeasurable cardinal we prove that in some forcing extension א ω is a strong limit cardinal and א ω+2 has the tree property. This improves a result of Matthew Foreman (see [2]).
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  9.  17
    The Strong Tree Property and the Failure of SCH.Jin Du - 2019 - Archive for Mathematical Logic 58 (7-8):867-875.
    Fontanella :193–207, 2014) showed that if \ is an increasing sequence of supercompacts and \, then the strong tree property holds at \. Building on a proof by Neeman, we show that the strong tree property at \ is consistent with \, where \ is singular strong limit of countable cofinality.
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  10.  32
    The Consistency Strength of Successive Cardinals with the Tree Property.Matthew Foreman, Menachem Magidor & Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (4):1837-1847.
    If ω n has the tree property for all $2 \leq n and $2^{ , then for all X ∈ H ℵ ω and $n exists.
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  11.  53
    Weak Covering and the Tree Property.Ralf-Dieter Schindler - 1999 - Archive for Mathematical Logic 38 (8):515-520.
    Suppose that there is no transitive model of ZFC + there is a strong cardinal, and let K denote the core model. It is shown that if $\delta$ has the tree property then $\delta^{+K} = \delta^+$ and $\delta$ is weakly compact in K.
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  12.  13
    The Consistency Strength of Successive Cardinals with the Tree Property.Matthew Foreman, Menachem Magidor & Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (4):1837-1847.
    If $\omega_n$ has the tree property for all $2 \leq n < \omega$ and $2^{<\aleph_{\omega}} = \aleph_{\omega}$, then for all $X \in H_{\aleph_{\omega}}$ and $n < \omega, M^#_n$ exists.
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  13.  21
    On the Consistency of the Definable Tree Property on ℵ.Amir Leshem - 2000 - Journal of Symbolic Logic 65 (3):1204 - 1214.
    In this paper we prove the equiconsistency of "Every ω 1 -tree which is first order definable over (H ω 1 ·ε) has a cofinal branch" with the existence of a Π 1 1 reflecting cardinal. We also prove that the addition of MA to the definable tree property increases the consistency strength to that of a weakly compact cardinal. Finally we comment on the generalization to higher cardinals.
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  14. Intellectual Property and Pharmaceutical Drugs: An Ethical Analysis.of Intellectual Property - 2008 - In Tom L. Beauchamp, Norman E. Bowie & Denis Gordon Arnold (eds.), Ethical Theory and Business. Pearson/Prentice Hall.
     
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  15.  11
    The Tree Property at the Successor of a Singular Limit of Measurable Cardinals.Mohammad Golshani - 2018 - Archive for Mathematical Logic 57 (1-2):3-25.
    Assume \ is a singular limit of \ supercompact cardinals, where \ is a limit ordinal. We present two methods for arranging the tree property to hold at \ while making \ the successor of the limit of the first \ measurable cardinals. The first method is then used to get, from the same assumptions, the tree property at \ with the failure of SCH at \. This extends results of Neeman and Sinapova. The second method (...)
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  16.  8
    The Tree Property Up to אω+1.Itay Neeman - 2014 - Journal of Symbolic Logic 79 (2):429-459.
  17.  41
    The Tree Property at Successors of Singular Cardinals.Menachem Magidor & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):385-404.
    Assuming some large cardinals, a model of ZFC is obtained in which $\aleph_{\omega+1}$ carries no Aronszajn trees. It is also shown that if $\lambda$ is a singular limit of strongly compact cardinals, then $\lambda^+$ carries no Aronszajn trees.
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  18.  4
    The Special Aronszajn Tree Property.Mohammad Golshani & Yair Hayut - forthcoming - Journal of Mathematical Logic:2050003.
    Assuming the existence of a proper class of supercompact cardinals, we force a generic extension in which, for every regular cardinal [Formula: see text], there are [Formula: see text]-Aronszajn trees, and all such trees are special.
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  19.  11
    The Tree Property at And.Dima Sinapova & Spencer Unger - 2018 - Journal of Symbolic Logic 83 (2):669-682.
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  20.  14
    The Tree Property Belowℵω⋅2.Spencer Unger - 2016 - Annals of Pure and Applied Logic 167 (3):247-261.
  21.  8
    The Tree Property at the ℵ 2 N 's and the Failure of SCH at ℵ Ω.Sy-David Friedman & Radek Honzik - 2015 - Annals of Pure and Applied Logic 166 (4):526-552.
  22.  11
    Destructibility of the Tree Property at ${\Aleph _{\Omega + 1}}$.Yair Hayut & Menachem Magidor - 2019 - Journal of Symbolic Logic 84 (2):621-631.
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  23.  11
    The Tree Property at ℵ Ω+1.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279-290.
    We show that given ω many supercompact cardinals, there is a generic extension in which there are no Aronszajn trees at ℵω+1. This is an improvement of the large cardinal assumptions. The previous hypothesis was a huge cardinal and ω many supercompact cardinals above it, in Magidor—Shelah [7].
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  24.  2
    The Strong Tree Property at Successors of Singular Cardinals.Laura Fontanella - 2014 - Journal of Symbolic Logic 79 (1):193-207.
  25.  10
    Destructibility of the Tree Property at אω+1.Yair Hayut & Menachem Magidor - forthcoming - Journal of Symbolic Logic:1-10.
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  26.  18
    Reflection of Stationary Sets and the Tree Property at the Successor of a Singular Cardinal.Laura Fontanella & Menachem Magidor - 2017 - Journal of Symbolic Logic 82 (1):272-291.
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  27.  16
    The Strong Tree Property and Weak Square.Yair Hayut & Spencer Unger - 2017 - Mathematical Logic Quarterly 63 (1-2):150-154.
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  28.  21
    Reviewed Work: Recent Papers on the Tree Property. Aronszajn Trees and Failure of the Singular Cardinal Hypothesis. Journal of Mathematical Logic, Vol. 9, No. 1 , The Tree Property at ℵ Ω+1. Journal of Symbolic Logic, Vol. 77, No. 1 , The Tree Property and the Failure of SCH at Uncountable Confinality. Archive for Mathematical Logic, Vol. 51, No. 5-6 , The Tree Property and the Failure of the Singular Cardinal Hypothesis at [Image]. Journal of Symbolic Logic, Vol. 77, No. 3 , Aronszajn Trees and the Successors of a Singular Cardinal. Archive for Mathematical Logic, Vol. 52, No. 5-6 , The Tree Property Up to ℵ Ω+1. Journal of Symbolic Logic. Vol. 79, No. 2 by Itay Neeman; Dima Sinapova; Spencer Unger. [REVIEW]Review by: James Cummings - 2015 - Bulletin of Symbolic Logic 21 (2):188-192.
  29.  1
    Indestructibility of the Tree Property.Radek Honzik & Šárka Stejskalová - forthcoming - Journal of Symbolic Logic:1-20.
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  30.  7
    The Tree Property at the Double Successor of a Singular Cardinal with a Larger Gap.Sy-David Friedman, Radek Honzik & Šárka Stejskalová - 2018 - Annals of Pure and Applied Logic 169 (6):548-564.
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  31.  8
    The Tree Property at Double Successors of Singular Cardinals of Uncountable Cofinality.Mohammad Golshani & Rahman Mohammadpour - 2018 - Annals of Pure and Applied Logic 169 (2):164-175.
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  32.  10
    Itay Neeman. Aronszajn Trees and Failure of the Singular Cardinal Hypothesis. Journal of Mathematical Logic, Vol. 9, No. 1 , Pp. 139–157. - Dima Sinapova. The Tree Property at אּω+1. Journal of Symbolic Logic, Vol. 77, No. 1 , Pp. 279–290. - Dima Sinapova. The Tree Property and the Failure of SCH at Uncountable Cofinality. Archive for Mathematical Logic, Vol. 51, No. 5-6 , Pp. 553–562. - Dima Sinapova. The Tree Property and the Failure of the Singular Cardinal Hypothesis at אּω2. Journal of Symbolic Logic, Vol. 77, No. 3 , Pp. 934–946. - Spencer Unger. Aronszajn Trees and the Successors of a Singular Cardinal. Archive for Mathematical Logic, Vol. 52, No. 5-6 , Pp. 483–496. - Itay Neeman. The Tree Property Up to אּω+1. Journal of Symbolic Logic. Vol. 79, No. 2 , Pp. 429–459. [REVIEW]James Cummings - 2015 - Bulletin of Symbolic Logic 21 (2):188-192.
  33.  5
    A Preservation Theorem for Theories Without the Tree Property of the First Kind.Jan Dobrowolski & Hyeungjoon Kim - 2017 - Mathematical Logic Quarterly 63 (6):536-543.
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  34.  4
    The Tree Property and the Continuum Function Below ℵω.Radek Honzik & Šárka Stejskalová - 2018 - Mathematical Logic Quarterly 64 (1-2):89-102.
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  35.  6
    Review: Uri Abraham, Aronszajn Trees on $Mathscr{N}2$ and $Mathscr{N}3$; James Cummings, Matthew Foreman, The Tree Property; Menachem Magidor, Saharon Shelah, The Tree Property at Successors of Singular Cardinals. [REVIEW]Arthur W. Apter - 2001 - Bulletin of Symbolic Logic 7 (2):283-285.
  36. REVIEWS-Three Papers on the Tree Property.Arthur W. Apter - 2001 - Bulletin of Symbolic Logic 7 (2):28-168.
  37. A Tukey Decomposition of ~K~a~P~P~aLambda and the Tree Property for Directed Sets.M. Karato - 2005 - Mathematical Logic Quarterly 51 (3):305.
     
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  38.  21
    Tree‐Properties for Ordered Sets.Olivier Esser & Roland Hinnion - 2002 - Mathematical Logic Quarterly 48 (2):213-219.
    In this paper, we study the notion of arborescent ordered sets, a generalizationof the notion of tree-property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be ℵ0-arborescent.
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  39.  25
    Aronszajn Trees and the Successors of a Singular Cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
    From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ ++ has the tree property. In particular this model has no special κ +-trees.
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  40.  7
    Strong Tree Properties for Small Cardinals.Laura Fontanella - 2013 - Journal of Symbolic Logic 78 (1):317-333.
    An inaccessible cardinal $\kappa$ is supercompact when $(\kappa, \lambda)$-ITP holds for all $\lambda\geq \kappa$. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where for every $n\geq 2$ and $\mu\geq \aleph_n$, we have $(\aleph_n, \mu)$-ITP.
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  41.  25
    Strong Tree Properties for Two Successive Cardinals.Laura Fontanella - 2012 - Archive for Mathematical Logic 51 (5-6):601-620.
    An inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove that if there is a model of ZFC with two supercompact cardinals, then there is a model of ZFC where simultaneously ${(\aleph_2, \mu)}$ -ITP and ${(\aleph_3, \mu')}$ -ITP hold, for all ${\mu\geq \aleph_2}$ and ${\mu'\geq \aleph_3}$.
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  42.  4
    Combinatorial Criteria for Ramifiable Ordered Sets.R. Hinnion & O. Esser - 2001 - Mathematical Logic Quarterly 47 (4):539-556.
    The tree-property and its variants make sense also for directed sets and even for partially ordered sets. A combinatoria approach is developed here, with characterizations and criteria involving adequate families of special substructures of directed sets. These substructures form a natural hierarchy that is also investigated.
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  43.  10
    Weak Partition Properties on Trees.Michael Hrušák, Petr Simon & Ondřej Zindulka - 2013 - Archive for Mathematical Logic 52 (5-6):543-567.
    We investigate the following weak Ramsey property of a cardinal κ: If χ is coloring of nodes of the tree κ <ω by countably many colors, call a tree ${T \subseteq \kappa^{ < \omega}}$ χ-homogeneous if the number of colors on each level of T is finite. Write ${\kappa \rightsquigarrow (\lambda)^{ < \omega}_{\omega}}$ to denote that for any such coloring there is a χ-homogeneous λ-branching tree of height ω. We prove, e.g., that if ${\kappa < \mathfrak{p}}$ (...)
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  44.  67
    Biodiversity, Biopiracy and Benefits: What Allegations of Biopiracy Tell Us About Intellectual Property.Chris Hamilton - 2006 - Developing World Bioethics 6 (3):158–173.
    ABSTRACTThis paper examines the concept of biopiracy, which initially emerged to challenge various aspects of the regime for intellectual property rights in living organisms, as well as related aspects pertaining to the ownership and apportioning of benefits from ‘genetic resources’ derived from the world’s biodiversity.This paper proposes that we take the allegation of biopiracy seriously due to the impact it has as an intervention which indexes a number of different, yet interrelated, problematizations of biodiversity, biotechnology and IPR. Using the (...)
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  45.  50
    Is Mind an Emergent Property?John-Michael Kuczynski - 1999 - Cogito 13 (2):117-119.
    It is often said that (M) "mind is an emergent property of matter." M is ambiguous, the reason being that, for all x and y, "x is an emergent property of y" has two distinct and mutually opposed meanings, namely: (i) x is a product of y (in the sense in which a chair is the product of the activity of a furniture-maker); and (ii) y is either identical or constitutive of x, but, relative to the information available (...)
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  46.  16
    On the Consistency of a Positive Theory.Olivier Esser - 1999 - Mathematical Logic Quarterly 45 (1):105-116.
    In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞+ + ACWF is a “strong” theory since “On (...)
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  47.  12
    Fixed-Points of Set-Continuous Operators.O. Esser, R. Hinnion & D. Dzierzgowski - 2000 - Mathematical Logic Quarterly 46 (2):183-194.
    In this paper, we study when a set-continuous operator has a fixed-point that is the intersection of a directed family. The framework of our study is the Kelley-Morse theory KMC– and the Gödel-Bernays theory GBC–, both theories including an Axiom of Choice and excluding the Axiom of Foundation. On the one hand, we prove a result concerning monotone operators in KMC– that cannot be proved in GBC–. On the other hand, we study conditions on directed superclasses in GBC– in order (...)
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  48.  10
    Tree-Properties for Ordered Sets.Olivier Esser & Roland Hinnion - 2002 - Mathematical Logic Quarterly 48 (2):213-219.
    In this paper, we study the notion of arborescent ordered sets, a generalizationof the notion of tree-property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be ℵ0-arborescent.
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  49.  7
    Large Cardinals and Ramifiability for Directed Sets.R. Hinnion & O. Esser - 2000 - Mathematical Logic Quarterly 46 (1):25-34.
    The notion of “ramifiability” , usually applied to cardinals, can be extended to directed sets and is put in relation here with familiar “large cardinal” properties.
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  50.  31
    An Variation for One Souslin Tree.Paul Larson - 1999 - Journal of Symbolic Logic 64 (1):81-98.
    We present a variation of the forcing S max as presented in Woodin [4]. Our forcing is a P max -style construction where each model condition selects one Souslin tree. In the extension there is a Souslin tree T G which is the direct limit of the selected Souslin trees in the models of the generic. In some sense, the generic extension is a maximal model of "there exists a minimal Souslin tree," with T G being this (...)
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