17 found
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  1. The Cofinality of Cardinal Invariants Related to Measure and Category.Tomek Bartoszynski, Jaime I. Ihoda & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (3):719-726.
    We prove that the following are consistent with ZFC. 1. 2 ω = ℵ ω 1 + K C = ℵ ω 1 + K B = K U = ω 2 (for measure and category simultaneously). 2. 2 ω = ℵ ω 1 = K C (L) + K C (M) = ω 2 . This concludes the discussion about the cofinality of K C.
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  2.  12
    On the Cofinality of the Smallest Covering of the Real Line by Meager Sets.Tomek Bartoszynski & Jaime I. Ihoda - 1989 - Journal of Symbolic Logic 54 (3):828-832.
    We prove that the cofinality of the smallest covering of R by meager sets is bigger than the additivity of measure.
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  3.  34
    The Cichoń Diagram.Tomek Bartoszyński, Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (2):401 - 423.
    We conclude the discussion of additivity, Baire number, uniformity, and covering for measure and category by constructing the remaining 5 models. Thus we complete the analysis of Cichon's diagram.
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  4.  13
    Closed Measure Zero Sets.Tomek Bartoszynski & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (2):93-110.
    Bartoszynski, T. and S. Shelah, Closed measure zero sets, Annals of Pure and Applied Logic 58 93–110. We study the relationship between the σ-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of the (...)
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  5.  4
    Jumping with Random Reals.Tomek Bartoszynski & Haim Judah - 1990 - Annals of Pure and Applied Logic 48 (3):197-213.
  6.  46
    Additivity Properties of Topological Diagonalizations.Tomek Bartoszynski, Saharon Shelah & Boaz Tsaban - 2003 - Journal of Symbolic Logic 68 (4):1254-1260.
    We answer a question of Just, Miller, Scheepers and Szeptycki whether certain diagonalization properties for sequences of open covers are provably closed under taking finite or countable unions.
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  7.  7
    Strongly Meager Sets Do Not Form an Ideal.Tomek Bartoszynski & Saharon Shelah - 2001 - Journal of Mathematical Logic 1 (1):1-34.
  8.  22
    Intersection of Ultrafilters May Have Measure Zero.Tomek Bartoszynski & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (4):221-226.
    We show that it is consistent with ZFC that the intersection of some family of less than ultrafilters have measure zero. This answers a question of D. Fremlin.
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  9.  39
    Strongly Meager Sets of Size Continuum.Tomek Bartoszynski & Saharon Shelah - 2003 - Archive for Mathematical Logic 42 (8):769-779.
    We will construct several models where there are no strongly meager sets of size 2ℵ0.
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  10.  54
    Adding One Random Real.Tomek Bartoszyński, Andrzej Rosłanowski & Saharon Shelah - 1996 - Journal of Symbolic Logic 61 (1):80-90.
    We study the cardinal invariants of measure and category after adding one random real. In particular, we show that the number of measure zero subsets of the plane which are necessary to cover graphs of all continuous functions may be large while the covering for measure is small.
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  11.  23
    Dual Borel Conjecture and Cohen Reals.Tomek Bartoszynski & Saharon Shelah - 2010 - Journal of Symbolic Logic 75 (4):1293-1310.
    We construct a model of ZFC satisfying the Dual Borel Conjecture in which there is a set of size ℵ₁ that does not have measure zero.
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  12.  6
    Miller Arnold W.. Descriptive Set Theory and Forcing. How to Prove Theorems About Borel Sets the Hard Way. Lecture Notes in Logic, No. 4. Springer, Berlin, Heidelberg, New York, Etc., 1995, Ii + 130 Pp. [REVIEW]Tomek Bartoszyński - 1997 - Journal of Symbolic Logic 62 (1):320-321.
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  13.  7
    Towards Martins Minimum.Tomek Bartoszynski & Andrzej Rosłlanowski - 2002 - Archive for Mathematical Logic 41 (1):65-82.
    No categories
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  14.  7
    1995–1996 Annual Meeting of the Association for Symbolic Logic.Tomek Bartoszynski, Harvey Friedman, Geoffrey Hellman, Bakhadyr Khoussainov, Phokion G. Kolaitis, Richard Shore, Charles Steinhorn, Mirna Dzamonja, Itay Neeman & Slawomir Solecki - 1996 - Bulletin of Symbolic Logic 2 (4):448-472.
  15.  7
    Review: Arnold W. Miller, Descriptive Set Theory and Forcing. How to Prove Theorems About Borel Sets the Hard Way. [REVIEW]Tomek Bartoszynski - 1997 - Journal of Symbolic Logic 62 (1):320-321.
  16.  2
    Strongly Meager and Strong Measure Zero Sets.Tomek Bartoszyński & Saharon Shelah - 2002 - Archive for Mathematical Logic 41 (3):245-250.
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  17. Mathematical Logic.Tomek Bartoszynski & Saharon Shelah - 2003 - Archive for Mathematical Logic 42:769-779.
     
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