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Transactions of the American Mathematical Society

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Partition theorems and ultrafilters


Authors: James E. Baumgartner and Alan D. Taylor
Journal: Trans. Amer. Math. Soc. 241 (1978), 283-309
MSC: Primary 04A20
DOI: https://doi.org/10.1090/S0002-9947-1978-0491193-1
MathSciNet review: 0491193
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Abstract: We introduce a class of ultrafilters on $ \omega $ called k-arrow ultrafilters and characterized by the partition relation $ U \to {(U,k)^2}$. These are studied in conjunction with P-points, Q-points, weakly Ramsey and Ramsey ultrafilters.


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  • [1] A. Blass, Ultrafilter mappings and their Dedekind cuts, Trans. Amer. Math. Soc. 188 (1974), 327-340. MR 0351822 (50:4310)
  • [2] -, Amalgamation of non-standard models of arithmetic, (preprint).
  • [3] D. Booth, Ultrafilters on a countable set, Ann. Math. Logic 2 (1970/71), 1-24. MR 43 #3104. MR 0277371 (43:3104)
  • [4] W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer-Verlag, Berlin and New York, 1974. MR 53 #135. MR 0396267 (53:135)
  • [5] E. Ellentuck, A new proof that analytic sets are Ramsey, J. Symbolic Logic 39 (1974), 163-165. MR 50 #1887. MR 0349393 (50:1887)
  • [6] A. Kanamori, Ultrafilters over uncountable cardinals, Thesis, Univ. of Cambridge, 1975.
  • [7] J. Ketonen, Ultrafilters over measurable cardinals, Fund. Math. 77 (1973), 257-269. MR 48 #8237. MR 0329897 (48:8237)
  • [8] K. Kunen, Ultrafilters and independent sets, Trans. Amer. Math. Soc. 172 (1972), 299-306. MR 47 #3170. MR 0314619 (47:3170)
  • [9] -, Some applications of iterated ultrapowers in set theory, Ann. Math. Logic 1 (1970), 179-227. MR 43 #3080. MR 0277346 (43:3080)
  • [10] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), 143-178. MR 42 #5787. MR 0270904 (42:5787)
  • [11] A. Mathias, Happy families, Ann. Math. Logic (to appear). MR 0491197 (58:10462)
  • [12] K. Milliken, Completely separable families and Ramsey's theorem, J. Combinatorial Theorey Ser. A 19 (1975), 318-334. MR 0403983 (53:7792)
  • [13] J. Nešetřil and V. Rödl, Partitions of finite relational and set systems, J. Combinatorial Theory Ser. A 22 (1977), 289-312. MR 0437351 (55:10283)
  • [14] C. W. Puritz, Ultrafilters and standard functions in non-standard arithmetic, Proc. London Math. Soc. (3) 22 (1971), 705-733. MR 44 #6474. MR 0289283 (44:6474)
  • [15] F. Rothberger, On some problems of Hausdorff and Sierpiński, Fund. Math. 35 (1948), 29-46. MR 10, 689. MR 0029958 (10:689a)
  • [16] F. Rowbottom, Some strong axioms of infinity incompatible with the axiom of constructibility, Ann. Math. Logic 3 (1971), 1-44. MR 48 #1928. MR 0323572 (48:1928)
  • [17] A. Taylor, P-points and Ramsey subsets of $ \omega $ (mimeographed).

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DOI: https://doi.org/10.1090/S0002-9947-1978-0491193-1
Article copyright: © Copyright 1978 American Mathematical Society

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