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Rado's conjecture and presaturation of the nonstationary ideal on ω1

Published online by Cambridge University Press:  12 March 2014

Qi Feng
Qi Feng*
Affiliation:
Institute of Mathematics, Academia Sinica, Beijing 100080, China E-mail: [email protected]
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Abstract

We prove that Rado's Conjecture implies that the nonstationary ideal on ω1 is presaturated.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 38 - 44
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1]Baumgartner, J. and Taylor, A., Saturation properties of ideals in generic extensions I, Transactions of the American Mathematical Society, vol. 270 (1982), pp. 587–574.CrossRefGoogle Scholar
[2]Feng, Q. and Jech, T., Projective stationary sets and strong reflection principles, Journal of the London Mathematical Society, to appear.Google Scholar
[3]Jech, T., Some combinatorial problems concerning uncountable cardinals, Annals of Mathematical Logic, vol. 5 (1973), pp. 165–198.CrossRefGoogle Scholar
[4]Jech, T., Set theory, Adademic Press, New York, 1978.Google Scholar
[5]Kueker, D., Countable approximations and Löwenheim-Skolem theorem, Annals of Mathematical Logic, vol. 11 (1977), pp. 57–103.CrossRefGoogle Scholar
[6]Rado, R., Theorems on intervals of ordered sets, Discrete Mathematics, vol. 35 (1981), pp. 199–201.CrossRefGoogle Scholar
[7]Steel, J., The core model iterability problem, to appear.Google Scholar
[8]Todorcčvić, S., Stationary sets, trees and continua, Publications, Institut Mathematicsématique, Beograd, vol. 43 (1981), pp. 249–262.Google Scholar
[9]Todorcčvić, S., On a conjecture of R. Rado, Journal of the London Mathematical Society, vol. 2 (1983), pp. 1–8.Google Scholar
[10]Todorcčvić, S., Partition relations for partially ordered sets, Acta Mathematka, vol. 155 (1985), pp. 1–25.Google Scholar
[11]Todorcčvić, S., Conjectures of Rado and Chang and cardinal arithmetic, Finite and infinite combinatorics in sets and logic (banff, ab, 1991), NATO Advanced Sciences Institute Series C: Mathematical and Physical Sciences, vol. 441, Kluwer Academic Publisher, Dordrecht, 1993, pp. 385–398.Google Scholar