There is no standard model of ZFC

Main Article Content

Jaykov Foukzon

Abstract

Main results are:(i) ConïƒZFC ∃standard model of ZFC,

(ii) let k be an inaccessible cardinal then ConïƒZFC +∃k)  [10]-[11].

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How to Cite
Foukzon, J. (2018). There is no standard model of ZFC. Journal of Global Research in Mathematical Archives(JGRMA), 5(1), 33–50. Retrieved from https://jgrma.com/index.php/jgrma/article/view/382
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Research Paper

References

E. Nelson.Warning Signs of a Possible Collapse of Contemporary Mathematics.

https://web.math.princeton.edu/~nelson/papers/warn.pdf

In Infinity: New Research Frontiers, by Michael Heller (Editor), W. Hugh Woodin

Pages 75–85, 2011. Published February 14th 2013 by Cambridge University

Press Hardcover, 311 pages. ISBN: 1107003873 (ISBN13: 9781107003873)

L. Henkin, "Completeness in the theory of types". Journal of

Symbolic Logic 15 (2): 81–91. doi:10.2307/2266967. JSTOR 2266967

M. Rossberg, "First-Order Logic, Second-Order Logic, and Completeness".

In V.Hendricks et al., eds. First-order logic revisited. Berlin: Logos-Verlag.

S. Shapiro, Foundations without Foundationalism: A Case for Second-order

Logic. Oxford University Press. ISBN 0-19-825029-0

A. Rayo and G. Uzquiano,Toward a Theory of Second-Order Consequence,

Notre Dame Journal of Formal Logic Volume 40, Number 3, Summer 1999.

J. Vaananen, Second-Order Logic and Foundations of Mathematics,

The Bulletin of Symbolic Logic, Vol.7, No. 4 (Dec., 2001), pp. 504-520.

G. Uzquiano, Quantification without a domain. New Waves in Philosophy of

Mathematics. Springer, 29 Sep 2009 - Philosophy - 327 pp.

ISBN 0230245196, 9780230245198

P. Cohen, Set Theory and the continuum hypothesis.Reprint of the

W. A. Benjamin,Inc.,New York,1966 edition. ISBN-13: 978-0486469218

E. Mendelson,Introduction to mathematical logic.1997. ISBN-10: 0412808307.

ISBN-13: 978-0412808302

2016 EUROPEAN SUMMER MEETING OF THE ASSOCIATION FOR

SYMBOLIC

LOGIC, LOGIC COLLOQUIUM ’16, Leeds, UK, July 31-August 6, 2016,

The Bulletin of Symbolic Logic Vol. 23, No. 2 (JUNE 2017), pp. 213-266

J.Foukzon, Inconsistent countable set in second order ZFC and unexistence of

the strongly inaccessible cardinals, pp.240.

J. Foukzon, Inconsistent Countable Set in Second Order ZFC and

Nonexistence of

the Strongly Inaccessible Cardinals,British Journal of Mathematics & Computer

Science, ISSN: 2231-0851,Vol.: 9, Issue.: 5

http://www.sciencedomain.org/abstract/9622

J. Foukzon,Generalized Lob’s Theorem.Strong Reflection Principles and

Large Cardinal Axioms. Consistency Results in Topology.

http://arxiv.org/abs/1301.5340v10

J.Foukzon,E. R. Men’kova,Generalized Löb’s Theorem. Strong Reflection

Principles and Large Cardinal Axioms, Advances in Pure Mathematics,

Vol.3 No.3, 2013.

http://dx.doi.org/10.4236/apm.2013.3053