On a conjecture of Tarski on products of cardinals

Jech, Thomas; Shelah, Saharon

doi:10.1090/S0002-9939-1991-1070525-1

On a conjecture of Tarski on products of cardinals

Authors: Thomas Jech and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 112 (1991), 1117-1124
MSC: Primary 03E10; Secondary 03E35
DOI: https://doi.org/10.1090/S0002-9939-1991-1070525-1
MathSciNet review: 1070525
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We look at an old conjecture of A. Tarski on cardinal arithmetic and show that if a counterexample exists, then there exists one of length ${\omega _1} + \omega$ .

[GH] Fred Galvin and András Hajnal, Inequalities for cardinal powers, Ann. of Math. (2) 101 (1975), 491–498. MR 376359, https://doi.org/10.2307/1970936
[M] Menachem Magidor, On the singular cardinals problem. I, Israel J. Math. 28 (1977), no. 1-2, 1–31. MR 491183, https://doi.org/10.1007/BF02759779
[ShA2] Saharon Shelah, Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin-New York, 1982. MR 675955
[Sh345] Saharon Shelah, Products of regular cardinals and cardinal invariants of products of Boolean algebras, Israel J. Math. 70 (1990), no. 2, 129–187. MR 1070264, https://doi.org/10.1007/BF02807866
[Sh355] -, $\aleph _{ \omega + 1}$ has a Jonsson algebra, preprint.
[T] A. Tarski, Quelques théorèmes sur les alephs, Fund. Math. 7 (1925), 1-14.