Ideals over ω 2 and combinatorical principles on ω 1
نویسنده
چکیده
An ideal I over Pκλ is said to be σ-strategically closed, proper or semiproper if the corresponding poset PI is σ-strategically closed, proper or semiproper, respectively. In this note we prove the following: • If there exists a σ-strategically closed, fine and κ-complete ideal over Pω2λ for some λ ≥ ω2 then ♦ω1 holds. • If there exists a proper, fine and κ-complete ideal over Pω2λ for some λ ≥ ω2 then CB, the completely bounding principle, does not hold. • If there exists a semiproper, fine and κ-complete ideal over Pω2λ for some λ ≥ ω2 then ♦ω1 does not hold.
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