Abstract
If there arek ++ eventually functions fromk + intok or if there arek ++ eventually different functions fromk + then uniform ultrafilters onk + are (k, k +)-regular.
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References
M. Benda,On reduced products and filters, Ann. of Math. Logic4 (1972), 1–29.
P. Erdös and A. Hajnal,Unsolved problems in set theory, Proc. of Symp. in Pure Math.III (D. Scott. ed.).
T. Jech,Some combinatorial problems concerning uncountable cardinals, Ann. of Math. Logic5 (1973), 165–198.
R. Jensen,Some combinatorial properties of L and V (to appear).
M. A. Jorgensen,Images of ultrafilters and cardinality of ultrapowers, Notices Amer. Math. Soc.18 (1971), 826.
H. J. Keisler,A survey of ultra-products, Proc. of Int. Congress 1964 (Y. Bar-Hillel, ed.), North-Holland 1965, pp. 112–126.
Ketonen,Some combinatorial principles (to appear).
D. W. Kueker,Löweheim-Skolem and interpolation theorems in infinitary languages, Bull. Amer, Math. J. Soc.78 (1972), 211–215.
K. Prikry,On a problem of Gillman and Keisler, Ann. of Math. Logic,2 (1970), 179–187.
K. Prikry,On descendingly complete ultrafilters (to appear).
A. Tarski,Ideale in vollständigen Mengenkörpen, Fund. Math.23 (1993), 45–63.
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The research of the first author was supported in part by NSF grant.
The second author is a Miller’s Fellow at the University of California in Berkeley.
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Benda, M., Ketonen, J. Regularity of ultrafilters. Israel J. Math. 17, 231–240 (1974). https://doi.org/10.1007/BF02756872
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DOI: https://doi.org/10.1007/BF02756872