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Juris Steprans [27]J. Steprans [8]
  1.  12
    On the Consistency of Some Partition Theorems for Continuous Colorings, and the Structure of ℵ 1 -Dense Real Order Types.J. Steprans, Uri Abraham, Matatyahu Rubin & Saharon Shelah - 2002 - Bulletin of Symbolic Logic 8 (2):303.
    We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ℵ 1 -dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ℵ 1 -dense subsets of R are isomorphic, is consistent. We e.g. prove Con). Let K H , be the set of order types of ℵ 1 -dense homogeneous subsets of (...)
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  2.  14
    Uri Abraham, Matatyahu Rubin, and Saharon Shelah. On the Consistency of Some Partition Theorems for Continuous Colorings, and the Structure of ℵ1-Dense Real Order Types. Annals of Pure and Applied Logic, Vol. 29 , Pp. 123–206. [REVIEW]J. Steprāns - 2002 - Bulletin of Symbolic Logic 8 (2):303-305.
  3.  13
    Paul C. Eklof and Alan H. Mekler. Almost Free Modules. Set-Theoretic Methods. North Holland Mathematical Library, Vol. 46. North-Holland, Amsterdam Etc. 1990, Xvi + 481 Pp. [REVIEW]Alan Dow & Juris Steprāns - 1995 - Journal of Symbolic Logic 60 (2):696-698.
  4.  12
    Just Winfried and Weese Martin. Discovering Modern Set Theory. I. The Basics. Graduate Studies in Mathematics, Vol. 8. American Mathematical Society, Providence 1996, Xvii + 210 Pp. [REVIEW]Juris Steprāns - 1996 - Journal of Symbolic Logic 61 (4):1393-1394.
  5. Combinatorial Properties of the Ideal ℬ2.J. Cichon, A. Roslanowski, J. Steprans & B. Weglorz - 1993 - Journal of Symbolic Logic 58 (1):42-54.
    By B2 we denote the σ-ideal of all subsets A of the Cantor set {0,1}ω such that for every infinite subset T of ω the restriction A∣{0,1}T is a proper subset of {0,1}T. In this paper we investigate set theoretical properties of this and similar ideals.
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  6. The Covering Numbers of Mycielski Ideals Are All Equal.Saharon Shelah & Juris Steprāns - 2001 - Journal of Symbolic Logic 66 (2):707-718.
    The Mycielski ideal M k is defined to consist of all sets $A \subseteq ^{\mathbb{N}}k$ such that $\{f \upharpoonright X: f \in A\} \neq ^Xk$ for all X ∈ [N] ℵ 0 . It will be shown that the covering numbers for these ideals are all equal. However, the covering numbers of the closely associated Roslanowski ideals will be shown to be consistently different.
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  7.  29
    Analytic and Coanalytic Families of Almost Disjoint Functions.Bart Kastermans, Juris Steprāns & Yi Zhang - 2008 - Journal of Symbolic Logic 73 (4):1158-1172.
    If F ⊆ NN is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable H ⊆ NN. no member of which is covered by finitely many functions from F, there is f ∈ F such that for all h ∈ H there are infinitely many integers k such that f(k) = h(k). However if V = L then there exists a coanalytic family of pairwise eventually different functions satisfying this strong maximality (...)
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  8. Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle.Juris Steprāns - 2005 - Bulletin of Symbolic Logic 11 (4):517-525.
    It is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.
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  9.  18
    A Very Discontinuous Borel Function.Juris Steprāns - 1993 - Journal of Symbolic Logic 58 (4):1268 - 1283.
    It is shown to be consistent that the reals are covered by ℵ1 meagre sets yet there is a Baire class 1 function which cannot be covered by fewer than ℵ2 continuous functions. A new cardinal invariant is introduced which corresponds to the least number of continuous functions required to cover a given function. This is characterized combinatorially. A forcing notion similar to, but not equivalent to, superperfect forcing is introduced.
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  10.  19
    Maximal Chains Inωω and Ultrapowers of the Integers.Saharon Shelah & Juris Steprāns - 1993 - Archive for Mathematical Logic 32 (5):305-319.
    Various questions posed by P. Nyikos concerning ultrafilters on ω and chains in the partial order (ω, <*) are answered. The main tool is the oracle chain condition and variations of it.
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  11.  8
    Extraspecial p-groups.Saharon Shelah & Juris Steprāns - 1987 - Annals of Pure and Applied Logic 34 (1):87-97.
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  12.  4
    The Number of Translates of a Closed Nowhere Dense Set Required to Cover a Polish Group.Arnold W. Miller & Juris Steprāns - 2006 - Annals of Pure and Applied Logic 140 (1):52-59.
    For a Polish group let be the minimal number of translates of a fixed closed nowhere dense subset of required to cover . For many locally compact this cardinal is known to be consistently larger than which is the smallest cardinality of a covering of the real line by meagre sets. It is shown that for several non-locally compact groups . For example the equality holds for the group of permutations of the integers, the additive group of a separable Banach (...)
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  13.  23
    Combinatorial Properties of the Ideal $Mathfrak{B}_2$.J. Cichon, A. Roslanowski, J. Steprans & B. Weglorz - 1993 - Journal of Symbolic Logic 58 (1):42-54.
    By $\mathfrak{B}_2$ we denote the $\sigma$-ideal of all subsets $A$ of the Cantor set $\{0,1\}^\omega$ such that for every infinite subset $T$ of $\omega$ the restriction $A\mid\{0,1\}^T$ is a proper subset of $\{0,1\}^T$. In this paper we investigate set theoretical properties of this and similar ideals.
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  14.  12
    Unions of Rectifiable Curves in Euclidean Space and the Covering Number of the Meagre Ideal.Juris Steprāns - 1999 - Journal of Symbolic Logic 64 (2):701-726.
    To any metric space it is possible to associate the cardinal invariant corresponding to the least number of rectifiable curves in the space whose union is not meagre. It is shown that this invariant can vary with the metric space considered, even when restricted to the class of convex subspaces of separable Banach spaces. As a corollary it is obtained that it is consistent with set theory that any set of reals of size ℵ 1 is meagre yet there are (...)
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  15.  22
    Towards a Structure Theory for Ideals on P Κ Λ.A Beginning for Structural Properties of Ideals on P Κ Λ.Alan D. Taylor, Donna M. Carr, Donald H. Pelletier, J. Steprans, S. Watson & William S. Zwicker - 1991 - Journal of Symbolic Logic 56 (3):1100.
  16.  36
    Cofinitary Groups, Almost Disjoint and Dominating Families.Michael Hrušák, Juris Steprans & Yi Zhang - 2001 - Journal of Symbolic Logic 66 (3):1259-1276.
    In this paper we show that it is consistent with ZFC that the cardinality of every maximal cofinitary group of Sym(ω) is strictly greater than the cardinal numbers o and a.
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  17.  14
    Review: Paul C. Eklof, Alan H. Mekler, Almost Free Modules. Set-Theoretic Methods. [REVIEW]Alan Dow & Juris Steprans - 1995 - Journal of Symbolic Logic 60 (2):696-698.
  18.  10
    S. Shelah. On Cardinal Invariants of the Continuum. Axiomatic Set Theory, Translated and Edited by D. A. Martin, J. Baumgartner, and S. Shelah, Contemporary Mathematics, Vol. 31. American Mathematical Society, Providence, 1984, Pp. 183–207. [REVIEW]Juris Steprāns - 2005 - Bulletin of Symbolic Logic 11 (3):451-453.
  19.  9
    Review: Winfried Just, Martin Weese, Discovering Modern Set Theory. I. The Basics. [REVIEW]Juris Steprans - 1996 - Journal of Symbolic Logic 61 (4):1393-1394.
  20.  7
    Countable Fréchetα 1-Spaces May Be First Countable.Alan Dow & Juris Stepräns - 1992 - Archive for Mathematical Logic 32 (1):33-50.
    It is shown to be consistent that countable, Fréchet,α 1-spaces are first countable. The result is obtained by using a countable support iteration of proper partial orders of lengthω 2.
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  21.  9
    Erratum.Saharon Shelah & Juris Steprāns - 1994 - Archive for Mathematical Logic 33 (2):167-168.
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  22.  9
    New Orleans Marriott and Sheraton New Orleans Hotels New Orleans, LA January 8–9, 2011.Jeremy Avigad, Ulrich W. Kohlenbach, Henry Towsner, Samson Abramsky, Andreas Blass, Larry Moss, Alf Onshuus Nino, Patrick Speissegger, Juris Steprans & Monica VanDieren - 2012 - Bulletin of Symbolic Logic 18 (1).
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  23.  10
    Review: Uri Abraham, Matatyahu Rubin, Saharon Shelah, On the Consistency of Some Partition Theorems for Continuous Colorings, and the Structure of $Aleph_1$-Dense Real Order Types. [REVIEW]J. Steprans - 2002 - Bulletin of Symbolic Logic 8 (2):303-305.
  24.  9
    Orthogonal Families of Real Sequences.Arnold W. Miller & Juris Steprans - 1998 - Journal of Symbolic Logic 63 (1):29-49.
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  25.  4
    Products of Sequential CLP-Compact Spaces Are CLP-Compact.Juris Steprāns - 2006 - Annals of Pure and Applied Logic 143 (1):155-157.
    It is shown that the product of finitely many sequential, CLP-compact spaces is CLP-compact.
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  26. REVIEWS-On Cardinal Invariants of the Continuum.S. Shelah & Juris Steprans - 2005 - Bulletin of Symbolic Logic 11 (3):451-453.
     
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  27. ASH, CJ, Categoricity in Hyperarithmetical Degrees BALDWIN, JT and HARRINGTON, L., Trivial Pursuit: Re-Marks on the Main Gap COOPER, SB and EPSTEIN, RL, Complementing Below Re-Cursively Enumerable Degrees.J. Steprans & S. Shelah - 1987 - Annals of Pure and Applied Logic 34:311.
  28. Axiomatic Set Theory.Juris Steprāns - 2005 - Bulletin of Symbolic Logic 11 (3):451-453.
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