Abstract
It is shown that the Magidor forcing to collapse the cofinality of a measurable cardinal that carries a length \(\omega _1\) sequence of normal ultrafilters, increasing in the Mitchell order, to \(\omega _1\), is subcomplete.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barwise, J.: Admissible Sets and Structures. Springer, Berlin (1975)
Fuchs, G.: On sequences generic in the sense of Magidor. J. Symb. Logic 79(4), 1286–1314 (2014)
Hayut, Y., Karagila, A.: Restrictions on forcings that change cofinalities. Arch. Math. Logic 55(3), 373–384 (2016)
Jensen, R.B.: Subproper and subcomplete forcing. Handwritten notes (2009). http://www.mathematik.hu-berlin.de/~raesch/org/jensen.html
Jensen, R.B.: Subcomplete forcing and \({{\cal{L}}}\)-forcing. In: Chong, C., Feng, Q., Slaman, T.A., Woodin, W.H., Yang, Y. (eds.) E-recursion, Forcing and \(C^*\)-Algebras. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, vol. 27, pp. 83–182. World Scientific, Singapore (2014)
Magidor, M.: Changing cofinality of cardinals. Fundam. Math. 99(1), 61–71 (1978)
Author information
Authors and Affiliations
Corresponding author
Additional information
The research for this paper was supported in part by PSC CUNY Research Grant 69656-00 47.
Rights and permissions
About this article
Cite this article
Fuchs, G. The subcompleteness of Magidor forcing. Arch. Math. Logic 57, 273–284 (2018). https://doi.org/10.1007/s00153-017-0568-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-017-0568-1