Generalized Löb’s Theorem. Strong Reflection Principles and Large Cardinal Axioms

Affiliation(s)

Israel Institute of Technology, Haifa, Israel.

Lomonosov Moscow State University, Moscow, Russia.

Israel Institute of Technology, Haifa, Israel.

Lomonosov Moscow State University, Moscow, Russia.

ABSTRACT

In this article, a possible generalization of the Lob’s theorem is considered. Main result is: let*κ* be an inaccessible cardinal, then

In this article, a possible generalization of the Lob’s theorem is considered. Main result is: let

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.

J. Foukzon and E. Men’kova, "Generalized Löb’s Theorem. Strong Reflection Principles and Large Cardinal Axioms,"

References

[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.

[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.