Abstract
We present a generalisation to ω 2 of Baumgartner’s forcing for adding a CUB subset of ω 1 with finite conditions.
This article was prepared during research visits to the Centre de Recerca Matematica, Bellaterra during the months of September 2003 and February–March 2005. Research support was provided by Forschungsprojekt Nr. P16334-NO5 des österreichischen Fonds zur Förderung der wissenschaftlichen Forschung. The author also wishes to thank Bill Mitchell, who independently obtained a similar result, for sharing his insights into this problem.
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References
Abraham, U. and Shelah, S. Forcing closed unbounded sets, Journal of Symbolic Logic, Vol. 48, pp. 643–657, 1983.
Baumgartner J., Harrington L. and Kleinberg E. Adding a closed unbounded set, Journal of Symbolic Logic, Vol. 41, pp. 481–482, 1976.
Friedman, S. Cardinal-preserving extensions, Journal of Symbolic Logic, Vol. 68, No. 4, pp. 1163–1170, 2003.
Friedman, S. and Krueger, J. Thin stationary sets and disjoint club sequences, to appear, Transactions of the American Mathematical Society, 2006.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Friedman, SD. (2006). Forcing with Finite Conditions. In: Bagaria, J., Todorcevic, S. (eds) Set Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7692-9_10
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DOI: https://doi.org/10.1007/3-7643-7692-9_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7691-8
Online ISBN: 978-3-7643-7692-5
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