A note on a lemma of Shelah concerning stationary sets

Authors:
Alan H. Mekler, Donald H. Pelletier and Alan D. Taylor

Journal:
Proc. Amer. Math. Soc. **83** (1981), 764-768

MSC:
Primary 04A20

DOI:
https://doi.org/10.1090/S0002-9939-1981-0630051-1

MathSciNet review:
630051

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an infinite cardinal, let be a nonprincipal ideal on and let . is the following property of ideals: for every and every pair of functions from into such that, for every , , there exists a set with such that . We prove that holds for every weakly selective ideal on any infinite cardinal (including ), and that holds for every -complete ideal on iff is not strongly inaccessible.

**[BTW]**J. Baumgartner, A. Taylor and S. Wagon,*Structural properties of ideals*, Dissertationes Math. (to appear).**[EM]**P. Eklof and A. Mekler,*Infinitary stationary logic and abelian groups*, Fund. Math. (to appear). MR**616732 (82j:03042)****[ER]**P. Erdös and R. Rado,*A partition calculus in set theory*, Bull. Amer. Math. Soc.**62**(1956), 427-489. MR**0081864 (18:458a)****[F]**G. Fodor,*Eine Bemerkung zur Theorie der regressiven Funktionen*, Acta Sci. Math. (Szeged)**17**(1956), 139-142. MR**0082450 (18:551d)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
04A20

Retrieve articles in all journals with MSC: 04A20

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0630051-1

Keywords:
Ideal,
stationary sets,
normal ideal,
weakly selective ideal

Article copyright:
© Copyright 1981
American Mathematical Society