Volume 2, Issue 3, June 2013, Page: 119-127
Strong Reflection Principles and Large Cardinal Axioms
J. Foukzon, Israel Institute of Technology, Haifa, Israel
E. R Men’kova, LomonosovMoscowStateUniversity, Moscow, Russia
Received: May 18, 2013;       Published: Jun. 10, 2013
DOI: 10.11648/j.pamj.20130203.12      View  2902      Downloads  120
Abstract
In this article an possible generalization of the Löb’s theorem is considered. We proved so-called uniform strong reflection principle corresponding to formal theories which has ω-models.Main result is: let κ be an inaccessible cardinal and H_κ is a set of all sets having hereditary size less than κ,then:"¬Con" ("ZFC+" ("V=" "H" _"κ" ) )
Keywords
Löb'stheorem, Second Gödelincompleteness Theorem, Consistency, Formal System, Uniform Reflection Principles, Ω-Model Of ZFC, Standard Model Of ZFC, Inaccessible Cardinal, Weakly Compact Cardinal
To cite this article
J. Foukzon, E. R Men’kova, Strong Reflection Principles and Large Cardinal Axioms, Pure and Applied Mathematics Journal. Vol. 2, No. 3, 2013, pp. 119-127. doi: 10.11648/j.pamj.20130203.12
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