4 Possible Pcf Algebras
نویسنده
چکیده
There exists a family {Bα}α<ω1 of sets of countable ordinals such that (1) maxBα = α, (2) if α ∈ Bβ then Bα ⊆ Bβ , (3) if λ ≤ α and λ is a limit ordinal then Bα ∩ λ is not in the ideal generated by the Bβ , β < α, and by the bounded subsets of λ, (4) there is a partition {An}n=0 of ω1 such that for every α and every n, Bα∩An is finite.
منابع مشابه
Applications of Pcf Theory Sh589
Abstract. We deal with several pcf problems; we characterize another version of exponentiation: number of κ-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 se...
متن کامل3 D ec 1 99 4 POSSIBLE PCF ALGEBRAS
There exists a family {Bα}α<ω1 of sets of countable ordinals such that (1) maxBα = α, (2) if α ∈ Bβ then Bα ⊆ Bβ , (3) if λ ≤ α and λ is a limit ordinal then Bα ∩ λ is not in the ideal generated by the Bβ , β < α, and by the bounded subsets of λ, (4) there is a partition {An}∞n=0 of ω1 such that for every α and every n, Bα∩An is finite.
متن کاملPossible pcf Algebras
There exists a family fB g <!1 of sets of countable ordinals such that (1) maxB = , (2) if 2 B then B B , (3) if and is a limit ordinal then B \ is not in the ideal generated by the B , < , and by the bounded subsets of , (4) there is a partition fAng1n=0 of !1 such that for every and every n; B \An is nite.
متن کاملDensities of Ultraproducts of Boolean Algebras
We answer three problems by J. D. Monk on cardinal invariants of Boolean algebras. Two of these are whether taking the algebraic density πA resp. the topological density dA of a Boolean algebra A commutes with formation of ultraproducts; the third one compares the number of endomorphisms and of ideals of a Boolean algebra. In set theoretic topology, considerable effort has been put into the stu...
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We answer three problems by J. D. Monk on cardinal invariants of Boolean algebras. Two of these are whether taking the algebraic density πA resp. the topological density dA of a Boolean algebra A commutes with formation of ultraproducts; the third one compares the number of endomorphisms and of ideals of a Boolean algebra. In set theoretic topology, considerable effort has been put into the stu...
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