A two-cardinal theorem and a combinatorial theorem

Author:
Saharon Shelah

Journal:
Proc. Amer. Math. Soc. **62** (1977), 134-136

MSC:
Primary 02H05; Secondary 04A20, 02H13

DOI:
https://doi.org/10.1090/S0002-9939-1977-0434800-6

MathSciNet review:
0434800

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a new two-cardinal theorem, e.g. . For this we prove a combinatorial theorem.

**[CK]**C. C. Chang and H. J. Keisler,*Model theory*, North-Holland, Amsterdam, 1973.**[H Le]**J. D. Halpern and A. Lévy,*The Boolean prime ideal theorem does not apply the axiom of choice*, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 83-134. MR**44**#1557.**[H La]**J. D. Halpern and H. Lauchli,*A partition theorem*, Trans. Amer. Math. Soc.**124**1966, 360-367. MR**34**#71. MR**0200172 (34:71)****[S1]**S. Shelah,*A two-cardinal theorem*, Proc. Amer. Math. Soc.**48**(1975), 207-213. MR**0357105 (50:9573)****[S2]**-,*Coloring without triangles and partition relation*, Israel Math.**20**(1975), 1-12. MR**0427073 (55:109)****[S3]**-,*Stability and number of non-isomorphic models*(in preparation).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0434800-6

Keywords:
Two-cardinal theorem,
partition calculus

Article copyright:
© Copyright 1977
American Mathematical Society