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4 results

  • USUBA’S PRINCIPLE $\mathrm {UB}_\lambda $ CAN FAIL AT SINGULAR CARDINALS

  • Part of
  • MOHAMMAD GOLSHANI, SAHARON SHELAH
  • Journal:
    The Journal of Symbolic Logic / Volume 89 / Issue 1 / March 2024
    Published online by Cambridge University Press:
    07 September 2023, pp. 195-203
    Print publication:
    March 2024
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  • We answer a question of Usuba by showing that the combinatorial principle $\mathrm {UB}_\lambda $ can fail at a singular cardinal. Furthermore, $\lambda $ can be taken to be $\aleph _\omega .$

  • THE PSEUDOPOWER DICHOTOMY

  • Part of
  • TODD EISWORTH
  • Journal:
    The Journal of Symbolic Logic / Volume 88 / Issue 4 / December 2023
    Published online by Cambridge University Press:
    10 January 2023, pp. 1655-1681
    Print publication:
    December 2023
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      • Open access
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  • We investigate pseudopowers of singular cardinals and deduce some consequences for covering numbers at singular cardinals of uncountable cofinality.

  • Generalized products of weakly m — n compact spaces, I

  • Part of
  • U. N. B. Dissanayake
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 33 / Issue 2 / October 1982
    Published online by Cambridge University Press:
    09 April 2009, pp. 143-151
    Print publication:
    October 1982
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  • A topological space X is said to be weakly-Lindelöf if and only if every open cover of X has a countable sub-family with dense union. We know that products of two Lindelöf spaces need not be weakly-Lindelöf. In this paper we obtain non-trivial sufficient conditions on small sub-products to ensure the producitivity of the property weakly-Lindelöf with respect to arbitrary products.