Abstract
We have already seen that there may exist \(2^{\mathfrak{c}}\) pairwise non-isomorphic Ramsey ultrafilters (see Proposition 14.10), that there may exist \(\mathfrak{c}\) Ramsey ultrafilters (see Proposition 23.6), and in the previous chapter we constructed a model in which there are no Ramsey ultrafilters (see Proposition 26.23). In this chapter, we conclude this issue by showing that for each cardinal κ with 0 ≤ κ ≤ ω 2, there is a model of ZFC in which there are exactly κ pairwise non-isomorphic Ramsey ultrafilters.
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References
David Chodounský, On the Katowice Problem, Dizertační práce (2011), Praha (Czech Republic).
Saharon Shelah, Proper and Improper Forcing, [Perspectives in Mathematical Logic], Springer-Verlag, Berlin, 1998.
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Halbeisen, L.J. (2017). How Many Ramsey Ultrafilters Exist?. In: Combinatorial Set Theory. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-60231-8_27
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DOI: https://doi.org/10.1007/978-3-319-60231-8_27
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