Diamond, Gch and Weak Square
نویسنده
چکیده
Shelah proved recently that if κ > ω and S ⊆ κ+ is a stationary set of ordinals of cofinality different from cf(κ), then 2κ = κ+ implies ♦κ+ (S). We show that for singular κ, an elaboration on his argument allows us to derive ♦κ+ (T ) from 2κ = κ+ + κ where T = {δ < κ+ | cf(δ) = cf(κ)}. This gives a strong restriction on the existence of saturated ideals on κ+.
منابع مشابه
The search for diamonds
Saharon Shelah. Middle Diamond. Archive for Mathematical Logic, vol. 44 (2005), pp. 527–560. Saharon Shelah. Diamonds. Proceedings of the American Mathematical Society, vol. 138 no. 6 (2010), pp. 2151–2161. Martin Zeman. Diamond, GCH and Weak Square. Proceedings of the American Mathematical Society, vol. 138 no. 5 (2010), pp. 1853–1859. The Continuum Hypothesis (CH) implies, and is in fact equi...
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تاریخ انتشار 2010