Published online by Cambridge University Press: 12 March 2014
We deal with several pcf problems: we characterize another version of exponentiation: maximal number of k-branches in a tree with λ nodes, deal with existence of independent sets in stable theories, possible cardinalities of ultraproducts and the depth of ultraproducts of Boolean Algebras. Also we give cardinal invariants for each λ with a pcf restriction and investigate further TD{f). The sections can be read independently, although there are some minor dependencies.
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