Modern Combinatorial Set Theory and Large Cardinal Properties
View Published Articles →01About 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
02Meet the Guest Editors
Our distinguished editors bring deep subject-matter expertise to curate high-quality research and ensure a rigorous peer-review process.
Guest Editor
Jaykov Foukzon
Israel Institute of Technology, Haifa, Israel, Israel
Guest Editor
Alex Potapov
Institute of Radioengineering and Electronics (IRE) of Russian Academy of Sciences, Moscow, Russian Federation
Guest Editor
Mohammad Hassan Anjom SHoa
University of Birjand, Birjand, Iran
Guest Editor
Aslam Malik
Department of Mathematics, University of the Punjab, Lahore, Pakistan
Guest Editor
Mohammed N. Murad
Math Department, Faculty of Science and Science Education, University of Sulaimani, Sulaimani, Iraq
03Published Articles
The following articles have been published in this special issue.
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Relevant First-Order Logic LP# and Curry’s Paradox Resolution
Issue: Volume 4, Issue 1-1, January 2015Pages: 6-12Received: 19 November 2014Accepted: 22 November 2014Published: 19 January 2015DOI: 10.11648/j.pamj.s.2015040101.12Downloads:Views: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
Issue: Volume 4, Issue 1-1, January 2015Pages: 1-5Received: 10 October 2014Accepted: 22 October 2014Published: 31 October 2014DOI: 10.11648/j.pamj.s.2015040101.11Downloads:Views: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.
