Pure and Applied Mathematics Journal

Special Issue

Modern Combinatorial Set Theory and Large Cardinal Properties

  • Submission Deadline: Dec. 20, 2014
  • Status: Submission Closed
About This Special Issue
The tools of modern combinatorial set theory, such as combinatorial principles, partition calculus, infinite trees, ultrapowers, forcing axioms, and large cardinal axioms, have been very successful in resolving problems in areas such as general topology, abstract functional analysis, measure theory, and algebra.

The topics include (but are not limited to):

1.Logical Foundations of Mathematics
2.Large Cardinal properties
3.Independence and Large Cardinals
4.Consistency of large cardinal axioms
5.Large cardinal axioms and Grothendieck universes
6.Implications between strong large cardinal axioms
7.Solovay hierarchy
8.Large Cardinals with forcing
9.Large Cardinals and Consistency Results in Topology
10.Infinitary languages and classification of uncountable structures
11.Applications of set theory to Banach spaces, algebra, topology and measure theory
12.Inner models of large cardinals and aspects of determinacy
13. Contemporary nonstandard analysis and possible generalizations
Guest Editors
  • Jaykov Foukzon

    Israel Institute of Technology, Haifa, Israel, Israel

  • Alex Potapov

    Institute of Radioengineering and Electronics (IRE) of Russian Academy of Sciences, Moscow, Russian Federation

  • Mohammad Hassan Anjom SHoa

    University of Birjand, Birjand, Iran

  • Aslam Malik

    Department of Mathematics, University of the Punjab, Lahore, Pakistan

  • Mohammed N. Murad

    Math Department, Faculty of Science and Science Education, University of Sulaimani, Sulaimani, Iraq

Published Articles
  • Relevant First-Order Logic LP# and Curry’s Paradox Resolution

    Jaykov Foukzon

    Issue: Volume 4, Issue 1-1, January 2015
    Pages: 6-12
    Received: Nov. 19, 2014
    Accepted: Nov. 22, 2014
    Published: Jan. 19, 2015
    DOI: 10.11648/j.pamj.s.2015040101.12
    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
  • Consistency Results in Topology and Homotopy Theory

    Jaykov Foukzon

    Issue: Volume 4, Issue 1-1, January 2015
    Pages: 1-5
    Received: Oct. 10, 2014
    Accepted: Oct. 22, 2014
    Published: Oct. 31, 2014
    DOI: 10.11648/j.pamj.s.2015040101.11
    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.