Abstract
We study non-homogeneity of quotients of Prikry and tree Prikry forcings with non-normal ultrafilters over some natural distributive forcing notions.
Similar content being viewed by others
References
Cummings, J.: Iterated forcing and elementary embeddings. In: Foreman, M., Kanamori, A. (eds.) Handbook of Set Theory, pp. 775–883. Springer, Dordrecht (2010)
Gitik, M.: Prikry-type forcings. In: Foreman, M., Kanamori, A. (eds.) Handbook of Set Theory, pp. 1351–1447. Springer, Dordrecht (2010)
Gitik, M.: Strange ultrafilters. Arch. Math. Logic (to appear)
Jech, T.: Set Theory. The Third Millennium Edition. Springer Monographs in Mathematics. Springer, Berlin (2003)
Koepke, P., Rasch, K., Schlicht, P.: A minimal Prikry-type forcing for singularizing a measurable cardinal. J. Symb. Logic 78(1), 85100 (2013)
Kunen, K.: Set Theory an Introduction to Independence Proofs, vol. 102. Elsevier, Amsterdam (2014)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
M. Gitik: The work was partially supported by Israel Science Foundation Grant No. 58/14. We are grateful to Arthur Apter for stimulating discussions on the subject of the paper. We would like to thank the referee for the useful remarks and corrections.
Rights and permissions
About this article
Cite this article
Gitik, M., Kaplan, E. Non-homogeneity of quotients of Prikry forcings. Arch. Math. Logic 58, 649–710 (2019). https://doi.org/10.1007/s00153-019-00659-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-019-00659-w