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P-ideal dichotomy and weak squares

Published online by Cambridge University Press:  12 March 2014

Dilip Raghavan
Dilip Raghavan*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada, E-mail: [email protected], URL: http://www.math.toronto.edu/raghavan
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Abstract

We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes □κ,ω for any uncountable κ. We also show that the P-ideal dichotomy implies the failure of □κ,<b provided that cf(κ) > ω1.

Keywords

P-ideal dichotomyweak square principleAronszajn tree
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 157 - 167
Copyright
Copyright © Association for Symbolic Logic 2013

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References

REFERENCES

[1]Cummings, J. and Magidor, M., Martin's maximum and weak square, Proceedings of the American Mathematical Society, vol. 139 (2011), pp. 3339–3348.CrossRefGoogle Scholar
[2]Moore, J. T., Set mapping reflection, Journal of Mathematical Logic, vol. 5 (2005), no. 1, pp. 87–97.CrossRefGoogle Scholar
[3]Schimmerling, E., A finite family weak square principle, this Journal, vol. 64 (1999), no. 3, pp. 1087–1110.Google Scholar
[4]Sharon, A., MRP and square principles, preprint, 2006.Google Scholar
[5]Todorčević, S., A note on the proper forcing axiom, Axiomatic set theory (Boulder, Colo., 1983), Contemporary Mathematics, vol. 31, American Mathematical Society, Providence, RI, 1984, pp. 209–218.CrossRefGoogle Scholar
[6]Todorčević, S., A dichotomy for P-ideals of countable sets, Fundamenta Mathematicae, vol. 166 (2000), no. 3, pp. 251–267.CrossRefGoogle Scholar
[7]Todorčević, S., Walks on ordinals and their characteristics, Progress in Mathematics, vol. 263, Birkháuser Verlag, Basel, 2007.CrossRefGoogle Scholar
[8]Todorčević, S., Combinatorial dichotomies in set theory, The Bulletin of Symbolic Logic, vol. 17 (2011), no. 1, pp. 1–72.CrossRefGoogle Scholar