Even more on partitioning triples of countable ordinals
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- by Albin L. Jones PDF
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Abstract:
We prove that $\omega _1 \to (\omega + \omega + 1, n)^3$ for all $n < \omega$.References
- J. Baumgartner and A. Hajnal, A proof (involving Martin’s axiom) of a partition relation, Fund. Math. 78 (1973), no. 3, 193–203. MR 319768, DOI 10.4064/fm-78-3-193-203
- Murray G. Bell, On the combinatorial principle $P({\mathfrak {c}})$, Fund. Math. 114 (1981), no. 2, 149–157. MR 643555, DOI 10.4064/fm-114-2-149-157
- P. Erdös and R. Rado, A partition calculus in set theory, Bull. Amer. Math. Soc. 62 (1956), 427–489. MR 81864, DOI 10.1090/S0002-9904-1956-10036-0
- D. H. Fremlin, Consequences of Martin’s axiom, Cambridge Tracts in Mathematics, vol. 84, Cambridge University Press, Cambridge, 1984. MR 780933, DOI 10.1017/CBO9780511896972
- A. Hajnal, Remarks on the theorem of W. P. Hanf, Fund. Math. 54 (1964), 109–113. MR 160734, DOI 10.4064/fm-54-1-109-113
- Albin L. Jones, A short proof of a partition relation for triples, Electron. J. Combin. 7 (2000), Research Paper 24, 9. MR 1755613
- Albin L. Jones, More on partitioning triples of countable ordinals, Proc. Amer. Math. Soc. 135 (2007), no. 4, 1197–1204. MR 2262926, DOI 10.1090/S0002-9939-06-08538-8
- Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
- E. C. Milner and K. Prikry, A partition theorem for triples, Proc. Amer. Math. Soc. 97 (1986), no. 3, 488–494. MR 840635, DOI 10.1090/S0002-9939-1986-0840635-8
- E. C. Milner and K. Prikry, A partition relation for triples using a model of Todorčević, Discrete Math. 95 (1991), no. 1-3, 183–191. Directions in infinite graph theory and combinatorics (Cambridge, 1989). MR 1141938, DOI 10.1016/0012-365X(91)90336-Z
- Jack H. Silver, A large cardinal in the constructible universe, Fund. Math. 69 (1970), 93–100. MR 274278, DOI 10.4064/fm-69-1-93-100
- Stevo Todorčević, Forcing positive partition relations, Trans. Amer. Math. Soc. 280 (1983), no. 2, 703–720. MR 716846, DOI 10.1090/S0002-9947-1983-0716846-0
Additional Information
- Albin L. Jones
- MR Author ID: 662270
- Email: albin.jones@gmail.com
- Received by editor(s): September 8, 2013
- Received by editor(s) in revised form: September 22, 2016
- Published electronically: April 17, 2018
- Communicated by: Mirna Džamonja
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3529-3539
- MSC (2010): Primary 03E02, 03E10; Secondary 03E05, 03E35, 03E60, 03E65
- DOI: https://doi.org/10.1090/proc/13503
- MathSciNet review: 3803677
Dedicated: Dedicated to the memory of James E. Baumgartner, my mentor and friend. I miss you, Jim.