APM  Vol.3 No.3 , May 2013
Generalized Löb’s Theorem. Strong Reflection Principles and Large Cardinal Axioms
In this article, a possible generalization of the Lob’s theorem is considered. Main result is: let κ be an inaccessible cardinal, then

Cite this paper
J. Foukzon and E. Men’kova, "Generalized Löb’s Theorem. Strong Reflection Principles and Large Cardinal Axioms," Advances in Pure Mathematics, Vol. 3 No. 3, 2013, pp. 368-373. doi: 10.4236/apm.2013.33053.
[1]   M. H. Lob, “Solution of a Problem of Leon Henkin,” The Journal of Symbolic Logic, Vol. 20, No. 2, 1955, pp. 115-118. doi:10.2307/2266895

[2]   J. Barwise, “Handbook of Mathematical Logic,” North-Holland Publishing Company, New York, 1977, p. 1151.

[3]   T. Drucker, “Perspectives on the History of Mathematical Logic,” Birkhauser, Boston, 2008, p. 191.

[4]   A. Marcja and C. Toffalori, “A Guide to Classical and Modern Model Theory (Series: Trends in Logic),” Springer, Berlin, 2003, p. 371.

[5]   F. W. Lawvere, C. Maurer and G. C. Wraith, “Model Theory and Topoi,” Springer, Berlin, 1975.

[6]   D. Marker, “Model Theory: An Introduction (Graduate Texts in Mathematics),” Springer, Berlin, 2002.

[7]   J. Foukzon, “Generalized Lob’s Theorem,” 2013. http://arxiv.org/abs/1301.5340

[8]   J. Foukzon, “An Possible Generalization of the Lob’s Theorem,” AMS Sectional Meeting AMS Special Session. Spring Western Sectional Meeting University of Colorado Boulder, Boulder, 13-14 April 2013. http://www.ams.org/amsmtgs/2210_abstracts/1089-03-60.pdf

[9]   P. Lindstrom, “First Order Predicate Logic with Generalized Quantifiers,” Theoria, Vol. 32, No. 3, 1966, pp. 186-195.

[10]   F. R. Drake, “Set Theory: An Introduction to Large Cardinal (Studies in Logic and the Foundations of Mathematics, Vol. 76),” North-Holland, New York, 1974.

[11]   A. Kanamori, “The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings,” 2nd Edition, Springer, Berlin, 2003.