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" ) )
| Published in | Pure and Applied Mathematics Journal (Volume 2, Issue 3) |
| DOI | 10.11648/j.pamj.20130203.12 |
| Page(s) | 119-127 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Löb'stheorem, Second Gödelincompleteness Theorem, Consistency, Formal System, Uniform Reflection Principles, Ω-Model Of ZFC, Standard Model Of ZFC, Inaccessible Cardinal, Weakly Compact Cardinal
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APA Style
J. Foukzon, E. R Men’kova. (2013). Strong Reflection Principles and Large Cardinal Axioms. Pure and Applied Mathematics Journal, 2(3), 119-127. https://doi.org/10.11648/j.pamj.20130203.12
ACS Style
J. Foukzon; E. R Men’kova. Strong Reflection Principles and Large Cardinal Axioms. Pure Appl. Math. J. 2013, 2(3), 119-127. doi: 10.11648/j.pamj.20130203.12
AMA Style
J. Foukzon, E. R Men’kova. Strong Reflection Principles and Large Cardinal Axioms. Pure Appl Math J. 2013;2(3):119-127. doi: 10.11648/j.pamj.20130203.12
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Download@article{10.11648/j.pamj.20130203.12,
author = {J. Foukzon and E. R Men’kova},
title = {Strong Reflection Principles and Large Cardinal Axioms},
journal = {Pure and Applied Mathematics Journal},
volume = {2},
number = {3},
pages = {119-127},
doi = {10.11648/j.pamj.20130203.12},
url = {https://doi.org/10.11648/j.pamj.20130203.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130203.12},
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" ) )},
year = {2013}
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TY - JOUR
T1 - Strong Reflection Principles and Large Cardinal Axioms
AU - J. Foukzon
AU - E. R Men’kova
Y1 - 2013/06/10
PY - 2013
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DO - 10.11648/j.pamj.20130203.12
T2 - Pure and Applied Mathematics Journal
JF - Pure and Applied Mathematics Journal
JO - Pure and Applied Mathematics Journal
SP - 119
EP - 127
PB - Science Publishing Group
SN - 2326-9812
UR - https://doi.org/10.11648/j.pamj.20130203.12
AB - 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" ) )
VL - 2
IS - 3
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