PCF and infinite free subsets

Saharon Shelah

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arXiv · math/9807177

PCF and infinite free subsets

Saharon Shelah

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Abstract

We give another proof that for every lambda >= beth_omega for every large enough regular kappa < beth_omega we have lambda^{[kappa]}= lambda, dealing with sufficient conditions for replacing beth_omega by aleph_omega. In section 2 we show that large pcf(a) implies existence of free sets. An example is that if pp(aleph_omega)> aleph_{omega_1} then for every algebra M of cardinality aleph_omega with countably many functions, for some a_n in M (for n< omega) we have a_n notin cl_M({a_l: l not= n, l ) and more general version, and from assumptions as in section 2 get results even for the non stationary ideal. Lastly, we deal with some other measurements of [lambda]^{>= theta} and give an application by a construction of a Boolean Algebra.

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BibTeX RIS

Saharon Shelah. 1998-07-15. PCF and infinite free subsets. https://arxiv.org/abs/math/9807177

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