Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-16T23:46:41.686Z Has data issue: false hasContentIssue false
  • English
  • Français

□ on the singular cardinals

Published online by Cambridge University Press:  12 March 2014

James Cummings  and
Sy-David Friedman
James Cummings
Affiliation:
Mathematical Sciences Department, Carnegie Mellon University, Pittsburgh PA 15215., USA, E-mail: [email protected]
Sy-David Friedman
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, Währinger Straβe 25, A-1090 Wien, Austria, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We give upper and lower bounds for the consistency strength of the failure of a combinatorial principle introduced by Jensen. Square on singular cardinals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1307 - 1314
Copyright
Copyright © Association for Symbolic Logic 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Burke, D., Generic embeddings and the failure of box, Proceedings of the American Mathematical Society, vol. 123 (1995), pp. 2867–2871.CrossRefGoogle Scholar
[2]Cummings, J. and Schimmerling, E., Indexed squares. Israel Journal of Mathematics, vol. 131 (2002), pp. 61–99.CrossRefGoogle Scholar
[3]Foreman, M. and Magidor, M., A very weak square principle, this Journal, vol. 62 (1997), pp. 175–196.Google Scholar
[4]Friedman, S. D., Large cardinals and L-like universes. Set theory: recent trends and applications. Quaderni di Matematica, Dept. Math. Seconda Univ. Napoli, Caserta, 2006. pp. 93–110.Google Scholar
[5]Friedman, S. D., Fine structure and class forcing, de Gruyter Series in Logic and Its Applications, 2000.CrossRefGoogle Scholar
[6]Jensen, R., The fine structure of the constructible hierarchy. Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308.CrossRefGoogle Scholar
[7]Jensen, R., Some results on square below 0-pistol, handwritten notes, 1993, Oxford.Google Scholar
[8]Mitchell, W., Indiscernibles, skies, and ideals in axiomatic set theory, Contemporary Mathematics 31, American Mathematical Society, Providence RI, 1984.Google Scholar
[9]Mitchell, W., The core model for sequences of measures I, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 95 (1984), pp. 229–260.CrossRefGoogle Scholar
[10]Mitchell, W., An introduction to inner models and large cardinals. Handbook of set theory.Google Scholar
[11]Schimmerling, E. and Zeman, M., A characterization of □k core models, Journal of Mathematical Logic, vol. 4 (2004), pp. 1–72.CrossRefGoogle Scholar
[12]Steel, J., PFA implies ADL(ℝ), this Journal, vol. 70 (2005). pp. 1255–1296.Google Scholar
[13]Welch, P., Combinatorial principles in the core model. D.Phil, thesis. Oxford University. 1979.Google Scholar
[14]Wylie, D., Condensation and square in a higher core model. Doctoral dissertation, Massachusetts Institute of Technology, 1990.Google Scholar
[15]Zeman, M., Das Kernmodell für nichtüberlappende Extender und seine Anwendungen. Ph.D. thesis, Humboldt University of Berlin, 1997.Google Scholar
[16]Zeman, M., Global square, circulated manuscript.Google Scholar