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COMBINING RESURRECTION AND MAXIMALITY
Part of:
Set theory
Published online by Cambridge University Press: 02 February 2021
Abstract
It is shown that the resurrection axiom and the maximality principle may be consistently combined for various iterable forcing classes. The extent to which resurrection and maximality overlap is explored via the local maximality principle.
MSC classification
Secondary:
03E55: Large cardinals
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- © The Association for Symbolic Logic 2021
Footnotes
Some of the material presented here is based on the author’s doctoral thesis [14], written at the Graduate Center of CUNY under the supervision of Gunter Fuchs.
References
REFERENCES
Bagaria, J., Bounded forcing axioms as principles of generic absoluteness. Archive for Mathematical Logic, vol. 39 (2000), pp. 393–401.CrossRefGoogle Scholar
Fuchs, G., Closed maximality principles: Implications, separations and combinations, this Journal, vol. 1 (2008), no. 73, pp. 276–308.Google Scholar
Fuchs, G., Combined maximality principles up to large cardinals, this Journal, vol. 74 (2009), no. 3, pp. 1015–1046.Google Scholar
Fuchs, G., Hiearchies of (virtual) resurrection axioms, this Journal, vol. 83 (2018), no. 1, pp. 283–325.Google Scholar
Fuchs, G., Hierarchies of forcing axioms, the continuum hypothesis and square principles, this Journal, vol. 83 (2018), no. 1, pp. 256–282.Google Scholar
Goldstern, M. and Shelah, S., The bounded proper forcing axiom, this Journal, vol. 60 (1995), no. 1, pp. 58–73.Google Scholar
Hamkins, J. D., A simple maximality principle, this Journal, vol. 68 (2003), no. 2, pp. 527–550.Google Scholar
Hamkins, J. D. and Johnstone, T. A., Resurrection axioms and uplifting cardinals. Archive for Mathematical Logic, vol. 53 (2014), no. 3, pp. 463–485.CrossRefGoogle Scholar
Hamkins, J. D. and Johnstone, T. A., Strongly uplifting cardinals and the boldface resurrection axioms. Archive for Mathematical Logic, vol. 56 (2017), pp. 1115–1133.CrossRefGoogle Scholar
Ikegami, D. and Trang, N., On a class of maximality principles. Archive for Mathematical Logic, vol. 57 (2018), pp. 713–725.CrossRefGoogle Scholar
Jensen, R. B., Subcomplete forcing and 
$\mathcal{L}$-forcing, E-Recursion, Forcing and C
${\vphantom{0}}^{*}$-Algebras (Chong, C., Feng, Q., Slaman, T. A., Woodin, W. H., and Yang, Y., editors), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, vol. 27, World Scientific, 2014, pp. 83–182.CrossRefGoogle Scholar
$\mathcal{L}$-forcing, E-Recursion, Forcing and C 
${\vphantom{0}}^{*}$-Algebras (Chong, C., Feng, Q., Slaman, T. A., Woodin, W. H., and Yang, Y., editors), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, vol. 27, World Scientific, 2014, pp. 83–182.CrossRefGoogle ScholarJensen, R. B., Forcing axioms compatible with CH, handwritten notes, 2009. Available at https://www.mathematik.hu-berlin.de/~raesch/org/jensen.html.Google Scholar
Leibman, G., Consistency strengths of modified maximality principles, Ph.D. thesis, The City University of New York, 2004.Google Scholar
Minden, K., On subcomplete forcing, Ph.D. thesis, The Graduate Center of the City University of New York, 2017. Available at https://arxiv.org/abs/1705.00386.Google Scholar
Stavi, J. and Väänänen, J., Reflection principles for the continuum, Logic and Algebra, AMS Contemporary Mathematics Series, vol. 302, American Mathematical Society, Providence, RI, 2002.CrossRefGoogle Scholar