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Natasha Dobrinen [19]Natasha L. Dobrinen [1]
  1.  11
    High Dimensional Ellentuck Spaces and Initial Chains in the Tukey Structure of Non-P-Points.Natasha Dobrinen - 2016 - Journal of Symbolic Logic 81 (1):237-263.
    The generic ultrafilter${\cal G}_2 $forced by${\cal P}\left/\left$was recently proved to be neither maximum nor minimum in the Tukey order of ultrafilters, but it was left open where exactly in the Tukey order it lies. We prove${\cal G}_2 $that is in fact Tukey minimal over its projected Ramsey ultrafilter. Furthermore, we prove that for each${\cal G}_2 $, the collection of all nonprincipal ultrafilters Tukey reducible to the generic ultrafilter${\cal G}_k $forced by${\cal P}\left/{\rm{Fin}}^{ \otimes k} $forms a chain of lengthk. Essential to (...)
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  2.  5
    Perfect Tree Forcings for Singular Cardinals.Natasha Dobrinen, Dan Hathaway & Karel Prikry - 2020 - Annals of Pure and Applied Logic 171 (9):102827.
  3.  14
    Topological Ramsey Spaces From Fraïssé Classes, Ramsey-Classification Theorems, and Initial Structures in the Tukey Types of P-Points.Natasha Dobrinen, José G. Mijares & Timothy Trujillo - 2017 - Archive for Mathematical Logic 56 (7-8):733-782.
    A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing the (...)
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  4.  16
    Homogeneous Iteration and Measure One Covering Relative to HOD.Natasha Dobrinen & Sy-David Friedman - 2008 - Archive for Mathematical Logic 47 (7-8):711-718.
    Relative to a hyperstrong cardinal, it is consistent that measure one covering fails relative to HOD. In fact it is consistent that there is a superstrong cardinal and for every regular cardinal κ, κ + is greater than κ + of HOD. The proof uses a very general lemma showing that homogeneity is preserved through certain reverse Easton iterations.
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  5.  40
    James Cummings and Ernest Schimmerling, Editors. Lecture Note Series of the London Mathematical Society, Vol. 406. Cambridge University Press, New York, Xi + 419 Pp. - Paul B. Larson, Peter Lumsdaine, and Yimu Yin. An Introduction to Pmax Forcing. Pp. 5–23. - Simon Thomas and Scott Schneider. Countable Borel Equivalence Relations. Pp. 25–62. - Ilijas Farah and Eric Wofsey. Set Theory and Operator Algebras. Pp. 63–119. - Justin Moore and David Milovich. A Tutorial on Set Mapping Reflection. Pp. 121–144. - Vladimir G. Pestov and Aleksandra Kwiatkowska. An Introduction to Hyperlinear and Sofic Groups. Pp. 145–185. - Itay Neeman and Spencer Unger. Aronszajn Trees and the SCH. Pp. 187–206. - Todd Eisworth, Justin Tatch Moore, and David Milovich. Iterated Forcing and the Continuum Hypothesis. Pp. 207–244. - Moti Gitik and Spencer Unger. Short Extender Forcing. Pp. 245–263. - Alexander S. Kechris and Robin D. Tucker-Drob. The Complexity of Classification Problems in Ergodic Theory. Pp. 265–29. [REVIEW]Natasha Dobrinen - 2014 - Bulletin of Symbolic Logic 20 (1):94-97.
  6.  21
    Almost Everywhere Domination.Natasha L. Dobrinen & Stephen G. Simpson - 2004 - Journal of Symbolic Logic 69 (3):914-922.
    A Turing degree a is said to be almost everywhere dominating if, for almost all $X \in 2^{\omega}$ with respect to the "fair coin" probability measure on $2^{\omega}$ , and for all g: $\omega \rightarrow \omega$ Turing reducible to X, there exists f: $\omega \rightarrow \omega$ of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly defined classes of Turing degrees. We relate this problem to some questions in (...)
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  7.  17
    Infinite-Dimensional Ellentuck Spaces and Ramsey-Classification Theorems.Natasha Dobrinen - 2016 - Journal of Mathematical Logic 16 (1):1650003.
    We extend the hierarchy of finite-dimensional Ellentuck spaces to infinite dimensions. Using uniform barriers [Formula: see text] on [Formula: see text] as the prototype structures, we construct a class of continuum many topological Ramsey spaces [Formula: see text] which are Ellentuck-like in nature, and form a linearly ordered hierarchy under projections. We prove new Ramsey-classification theorems for equivalence relations on fronts, and hence also on barriers, on the spaces [Formula: see text], extending the Pudlák–Rödl theorem for barriers on the Ellentuck (...)
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  8.  27
    The Next Best Thing to a P-Point.Andreas Blass, Natasha Dobrinen & Dilip Raghavan - 2015 - Journal of Symbolic Logic 80 (3):866-900.
  9.  10
    Κ-Stationary Subsets of Pκ+Λ, Infinitary Games, and Distributive Laws in Boolean Algebras.Natasha Dobrinen - 2008 - Journal of Symbolic Logic 73 (1):238 - 260.
    We characterize the (κ, Λ, < μ)-distributive law in Boolean algebras in terms of cut and choose games $\scr{G}_{<\mu}^{\kappa}(\lambda)$ , when μ ≤ κ ≤ Λ and κ<κ = κ. This builds on previous work to yield game-theoretic characterizations of distributive laws for almost all triples of cardinals κ, Λ, μ with μ ≤ Λ, under GCH. In the case when μ ≤ κ ≤ Λ and κ<κ = κ, we show that it is necessary to consider whether the κ-stationarity (...)
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  10.  11
    Internal Consistency and Global Co-Stationarity of the Ground Model.Natasha Dobrinen & Sy-David Friedman - 2008 - Journal of Symbolic Logic 73 (2):512 - 521.
    Global co-stationarity of the ground model from an N₂-c.c, forcing which adds a new subset of N₁ is internally consistent relative to an ω₁-Erdös hyperstrong cardinal and a sufficiently large measurable above.
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  11.  13
    Co-Stationarity of the Ground Model.Natasha Dobrinen & Sy-David Friedman - 2006 - Journal of Symbolic Logic 71 (3):1029 - 1043.
    This paper investigates when it is possible for a partial ordering P to force Pκ(λ) \ V to be stationary in VP. It follows from a result of Gitik that whenever P adds a new real, then Pκ(λ) \ V is stationary in VP for each regular uncountable cardinal κ in VP and all cardinals λ > κ in VP [4]. However, a covering theorem of Magidor implies that when no new ω-sequences are added, large cardinals become necessary [7]. The (...)
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  12.  3
    The Ramsey Theory of the Universal Homogeneous Triangle-Free Graph.Natasha Dobrinen - forthcoming - Journal of Mathematical Logic.
    The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math.38(1) (1971) 69–83] and denoted H3, is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.I, eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), pp. 585–595] and culminating in work (...)
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  13.  4
    Forcing and the Halpern–Läuchli Theorem.Natasha Dobrinen & Daniel Hathaway - 2020 - Journal of Symbolic Logic 85 (1):87-102.
    We investigate the effects of various forcings on several forms of the Halpern– Läuchli theorem. For inaccessible κ, we show they are preserved by forcings of size less than κ. Combining this with work of Zhang in [17] yields that the polarized partition relations associated with finite products of the κ-rationals are preserved by all forcings of size less than κ over models satisfying the Halpern– Läuchli theorem at κ. We also show that the Halpern–Läuchli theorem is preserved by <κ-closed (...)
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  14.  5
    Κ-Stationary Subsets Of.Natasha Dobrinen - 2008 - Journal of Symbolic Logic 73 (1):238-260.
    We characterize the -distributive law in Boolean algebras in terms of cut and choose games.
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  15.  5
    Steven Givant and Paul Halmos. Introduction to Boolean Algebras. Undergraduate Texts in Mathematics. Springer, 2009, Xiv + 574 Pp. [REVIEW]Natasha Dobrinen - 2010 - Bulletin of Symbolic Logic 16 (2):281-282.
  16.  2
    Herbert B. Enderton. A Mathematical Introduction to Logic. Harcourt/Academic Press, New York and London, 2001 , Xii + 317 Pp. [REVIEW]Natasha Dobrinen - 2003 - Bulletin of Symbolic Logic 9 (3):406-407.
  17.  9
    Gainesville, Florida March 10–13, 2007.Michael Benedikt, Andreas Blass, Natasha Dobrinen, Noam Greenberg, Denis R. Hirschfeldt, Salma Kuhlmann, Hannes Leitgeb, William J. Mitchell & Thomas Wilke - 2007 - Bulletin of Symbolic Logic 13 (3).
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  18.  6
    The Hyper-Weak Distributive Law and a Related Game in Boolean Algebras.James Cummings & Natasha Dobrinen - 2007 - Annals of Pure and Applied Logic 149 (1):14-24.
    We discuss the relationship between various weak distributive laws and games in Boolean algebras. In the first part we give some game characterizations for certain forms of Prikry’s “hyper-weak distributive laws”, and in the second part we construct Suslin algebras in which neither player wins a certain hyper-weak distributivity game. We conclude that in the constructible universe L, all the distributivity games considered in this paper may be undetermined.
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