Pure and Applied Mathematics Journal

Volume 4, Issue 1, January 2015

  • Consistency Results in Topology and Homotopy Theory

    Jaykov Foukzon

    Issue: Volume 4, Issue 1-1, January 2015
    Pages: 1-5
    Received: 10 October 2014
    Accepted: 22 October 2014
    Published: 31 October 2014
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    This article belongs to the Special Issue Modern Combinatorial Set Theory and Large Cardinal Properties
    Abstract: Main results is: (1) let κ be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = Hk )), (2) there is a Lindelöf T3 indestructible space of pseudocharacter ≤N1 and size N2 in L.
  • Relevant First-Order Logic LP# and Curry’s Paradox Resolution

    Jaykov Foukzon

    Issue: Volume 4, Issue 1-1, January 2015
    Pages: 6-12
    Received: 19 November 2014
    Accepted: 22 November 2014
    Published: 19 January 2015
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    This article belongs to the Special Issue Modern Combinatorial Set Theory and Large Cardinal Properties
    Abstract: In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without reject... Show More