Is it still open whether ZFC+GCH is consistent with the statement that there are no $\aleph_2$-Suslin trees?
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asked Nov 21, 2013 at 16:25
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From http://www.users.muohio.edu/larsonpb/kly_guessing.pdf (pdf 9 of 16):
Note that the consistency of GCH + "no $\omega_{2}$-Suslin-trees" is still an open question. ...this old question is now more open than ever.
As best as I can tell, the matter has not been settled in the six years since the published paper above.
Citation:
König, B., Larson, P., & Yoshinobu, Y. (2007). Guessing clubs in the generalized club filter. Fundamenta Mathematicae, 195(2), 177-191.
answered Nov 21, 2013 at 17:03