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The tree property at ℵω+2

  • Sy-David Friedman (a1) and Ajdin Halilović (a2)


Assuming the existence of a weakly compact hypermeasurable cardinal we prove that in some forcing extension ℵω is a strong limit cardinal and ℵω+2 has the tree property. This improves a result of Matthew Foreman (see [2]).



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[1]Abraham, U., Aronszajn trees on ℵ2 and ℵ3, Annals of Pure and Applied Logic, vol. 24 (1983), pp. 213230.
[2]Cummings, J. and Foreman, M., The tree property, Advances in Mathematics, vol. 133 (1998), pp. 132.
[3]Dobrinen, N. and Friedman, S., The consistency strength of the tree property at the double successor of a measurable, Fundamenta Mathematicae, vol. 208 (2010), pp. 123153.
[4]Foreman, M., Magidor, M., and Schindler, R., The consistency strength of successive cardinals with the tree property, this Journal, vol. 66 (2001), pp. 18371847.
[5]Gitik, M., The negation of sch from o(κ) = κ++, Annals of Pure and Applied Logic, vol. 43 (1989), pp. 209234.
[6]Kanamori, A., Perfect set forcing for uncountable cardinals, Annals of Mathematical Logic, vol. 19 (1980), pp. 97114.
[7]Magidor, M. and Shelah, S., The tree property at successors of singular cardinals, Archive for Mathematical Logic, vol. 35 (1996), pp. 385404.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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