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Marcia Groszek [13]Marcia J. Groszek [12]M. Groszek [2]
  1.  39
    Reverse mathematics and Ramsey's property for trees.Jared Corduan, Marcia J. Groszek & Joseph R. Mileti - 2010 - Journal of Symbolic Logic 75 (3):945-954.
    We show, relative to the base theory RCA₀: A nontrivial tree satisfies Ramsey's Theorem only if it is biembeddable with the complete binary tree. There is a class of partial orderings for which Ramsey's Theorem for pairs is equivalent to ACA₀. Ramsey's Theorem for singletons for the complete binary tree is stronger than $B\sum_{2}^{0}$ , hence stronger than Ramsey's Theorem for singletons for ω. These results lead to extensions of results, or answers to questions, of Chubb, Hirst, and McNicholl [3].
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  2.  65
    An almost deep degree.Peter Cholak, Marcia Groszek & Theodore Slaman - 2001 - Journal of Symbolic Logic 66 (2):881-901.
    We show there is a non-recursive r.e. set A such that if W is any low r.e. set, then the join W $\oplus$ A is also low. That is, A is "almost deep". This answers a question of Jockusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.).
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  3. Combinatorics on ideals and forcing with trees.Marcia J. Groszek - 1987 - Journal of Symbolic Logic 52 (3):582-593.
    Classes of forcings which add a real by forcing with branching conditions are examined, and conditions are found which guarantee that the generic real is of minimal degree over the ground model. An application is made to almost-disjoint coding via a real of minimal degree.
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  4.  25
    Uncountable superperfect forcing and minimality.Elizabeth Theta Brown & Marcia J. Groszek - 2006 - Annals of Pure and Applied Logic 144 (1-3):73-82.
    Uncountable superperfect forcing is tree forcing on regular uncountable cardinals κ with κ<κ=κ, using trees in which the heights of nodes that split along any branch in the tree form a club set, and such that any node in the tree with more than one immediate extension has measure-one-many extensions, where the measure is relative to some κ-complete, nonprincipal normal filter F. This forcing adds a generic of minimal degree if and only if F is κ-saturated.
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  5.  52
    A basis theorem for perfect sets.Marcia J. Groszek & Theodore A. Slaman - 1998 - Bulletin of Symbolic Logic 4 (2):204-209.
    We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair $M\subset N$ of models of set theory implying that every perfect set in N has an element in N which is not in M.
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  6.  56
    The Sacks density theorem and Σ2-bounding.Marcia J. Groszek, Michael E. Mytilinaios & Theodore A. Slaman - 1996 - Journal of Symbolic Logic 61 (2):450 - 467.
    The Sacks Density Theorem [7] states that the Turing degrees of the recursively enumerable sets are dense. We show that the Density Theorem holds in every model of P - + BΣ 2 . The proof has two components: a lemma that in any model of P - + BΣ 2 , if B is recursively enumerable and incomplete then IΣ 1 holds relative to B and an adaptation of Shore's [9] blocking technique in α-recursion theory to models of arithmetic.
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  7.  22
    Applications of iterated perfect set forcing.Marcia J. Groszek - 1988 - Annals of Pure and Applied Logic 39 (1):19-53.
  8. Downey, R., Fiiredi, Z., Jockusch Jr., CG and Ruhel, LA.W. I. Gasarch, A. C. Y. Lee, M. Groszek, T. Hummel, V. S. Harizanov, H. Ishihara, B. Khoussainov, A. Nerode, I. Kalantari & L. Welch - 1998 - Annals of Pure and Applied Logic 93:263.
     
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  9. Ω*1 as an initial segment of the c-degrees.Marcia Groszek - 1994 - Journal of Symbolic Logic 59 (3):956 - 976.
    By an "inverse iteration" of Sacks forcing over a model of V = L, we produce a model in which the degrees of constructibility of nonconstructible reals have order type ω 1 *.
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  10.  12
    Grigorieff Forcing on Uncountable Cardinals Does Not Add a Generic of Minimal Degree.Brooke M. Andersen & Marcia J. Groszek - 2009 - Notre Dame Journal of Formal Logic 50 (2):195-200.
    Grigorieff showed that forcing to add a subset of ω using partial functions with suitably chosen domains can add a generic real of minimal degree. We show that forcing with partial functions to add a subset of an uncountable κ without adding a real never adds a generic of minimal degree. This is in contrast to forcing using branching conditions, as shown by Brown and Groszek.
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  11.  27
    Reverse Mathematics and Ramsey Properties of Partial Orderings.Jared Corduan & Marcia Groszek - 2016 - Notre Dame Journal of Formal Logic 57 (1):1-25.
    A partial ordering $\mathbb{P}$ is $n$-Ramsey if, for every coloring of $n$-element chains from $\mathbb{P}$ in finitely many colors, $\mathbb{P}$ has a homogeneous subordering isomorphic to $\mathbb{P}$. In their paper on Ramsey properties of the complete binary tree, Chubb, Hirst, and McNicholl ask about Ramsey properties of other partial orderings. They also ask whether there is some Ramsey property for pairs equivalent to $\mathit{ACA}_{0}$ over $\mathit{RCA}_{0}$. A characterization theorem for finite-level partial orderings with Ramsey properties has been proven by the (...)
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  12. Sheraton New Orleans Hotel, New Orleans, Louisiana January 12–13, 2001.James Cummings, Marcia Groszek & Dave Marker - 2001 - Bulletin of Symbolic Logic 7 (3).
     
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  13.  10
    Schmerl decompositions in first order arithmetic.François Dorais, Zachary Evans, Marcia Groszek, Seth Harris & Theodore Slaman - 2019 - Annals of Pure and Applied Logic 170 (12):102717.
  14.  54
    New Orleans Marriott and Sheraton New Orleans New Orleans, Louisiana January 7–8, 2007.Matthew Foreman, Su Gao, Valentina Harizanov, Ulrich Kohlenbach, Michael Rathjen, Reed Solomon, Carol Wood & Marcia Groszek - 2007 - Bulletin of Symbolic Logic 13 (3).
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  15.  33
    Π10 classes and minimal degrees.Marcia J. Groszek & Theodore A. Slaman - 1997 - Annals of Pure and Applied Logic 87 (2):117-144.
    Theorem. There is a non-empty Π10 class of reals, each of which computes a real of minimal degree. Corollary. WKL “there is a minimal Turing degree”. This answers a question of H. Friedman and S. Simpson.
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  16.  13
    ∑2-constructions and I∑1.Marcia Groszek & Tamara Hummel - 1998 - Annals of Pure and Applied Logic 93 (1-3):83-101.
    The consistency strength of the ∑2 priority method is I∑2, yet classical theorems proven by this method have been proved from I∑1. Is there a statement about the structure of the r.e. degrees that can be proved using a ∑2 argument and cannot be proved from I∑1?We rule out statements in the language of partial orderings of the form …[], where is quantifier-free, by showing that the following can be proved in I∑1.If P is any recursive partial ordering with a (...)
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  17.  3
    In honor of James E. Baumgartner’s sixtieth birthday.M. Groszek - 2006 - Annals of Pure and Applied Logic 144 (1-3):1.
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  18.  38
    Π10 classes and minimal degrees.Marcia J. Groszek & Theodore A. Slaman - 1997 - Annals of Pure and Applied Logic 87 (2):117-144.
  19.  13
    $omega^ast_1$ as an Initial Segment of the $c$-Degrees.Marcia Groszek - 1994 - Journal of Symbolic Logic 59 (3):956-976.
    By an "inverse iteration" of Sacks forcing over a model of $V = L$, we produce a model in which the degrees of constructibility of nonconstructible reals have order type $\omega_1^\ast$.
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  20.  8
    ∑2-constructions and I∑1.Marcia Groszek & Tamara Hummel - 1998 - Annals of Pure and Applied Logic 93 (1-3):83-101.
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  21.  10
    ∑2-constructions and I∑1.Marcia Groszek & Tamara Hummel - 1998 - Annals of Pure and Applied Logic 93 (1-3):83-101.
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  22.  20
    The implicitly constructible universe.Marcia J. Groszek & Joel David Hamkins - 2019 - Journal of Symbolic Logic 84 (4):1403-1421.
    We answer several questions posed by Hamkins and Leahy concerning the implicitly constructible universe Imp, which they introduced in [5]. Specifically, we show that it is relatively consistent with ZFC that $$Imp = \neg {\rm{CH}}$$, that $Imp \ne {\rm{HOD}}$, and that $$Imp \models V \ne Imp$$, or in other words, that $\left^{Imp} \ne Imp$.
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