Let κ < λ be regular cardinals. We say that an embedding j : V → M with critical point κ is λ-tall if λ < j(κ) and M is closed under κ-sequences in V . Silver showed that GCH can fail at a measurable cardinal κ, starting with κ being κ++-supercompact. Later, Woodin improved this result, starting from the optimal hypothesis of a κ++-tall measurable cardinal κ. Now more generally, suppose that κ ...

Suppose κ = cf(κ), λ > cf(λ) = κ and λ = λ. We prove that there exist a sequence 〈Bi : i < κ〉 of Boolean algebras and an ultrafilterD on κ so that λ = ∏ i<κ Depth(Bi)/D < Depth ( ∏ i<κ Bi/D) = λ . An identical result holds also for Length. The proof is carried in ZFC, and it holds even above large cardinals. 2010 Mathematics Subject Classification. Primary: 06E05, 03G05. Secondary: 03E45.

ضرورت دسترسی به کاربردهای وسیع تصاویر ابرطیفی سبب توسعة سیستم‌های تصویربرداری نوآورانه و اقتصادی در ثبت این شده است. به‌منظور استفاده از تصاویر، لازم است ارتباط هندسی دقیقی میان آنها فضای زمین برقرار شود فرایند نیازمند نقاط کنترلی بسیاری نکته راهکارهای اصلاح منطبق با ساختار هریک دوربین‌ها را بارز می‌کند. سنجندة (nm 400-1000) BaySpec OCI-F یکی نوآورانه‌ای که هندسة پوش‌بروم دریافت سنجنده، علاوه‌ب...

We show that the reduced cofinality of the nonstationary ideal NSκ on a regular uncountable cardinal κ may be less than its cofinality, where the reduced cofinality of NSκ is the least cardinality of any family F of nonstationary subsets of κ such that every nonstationary subset of κ can be covered by less than κ many members of F . For this we investigate connections of the various cofinalitie...

Change first the cofinality of κ to ω by adding a Prikry sequence ⟨κn | n < ω⟩ such that each κn is κ +n+2 n –strong. Then use the short extenders forcing which adds κ +ω+2 many cofinal ω-sequences to κ (after the preparation or simultaneously with it). All cardinals will be preserved then. If one does not care about falling of κ, then preform Gap 2 short extenders forcing. As a result κ will t...

Based on the κ-deformed functions (κ-exponential and κ-logarithm) and associated multiplication operation (κ-product) introduced by Kaniadakis (Phys. Rev. E 66 (2002) 056125), we present another one-parameter generalization of Gauss’ law of error. The likelihood function in Gauss’ law of error is generalized by means of the κ-product. This κ-generalized maximum likelihood principle leads to the...

Let κ, λ be regular uncountable cardinals such that λ > κ+ is not a successor of a singular cardinal of low cofinality. We construct a generic extension with s(κ) = λ starting from a ground model in which o(κ) = λ and prove that assuming ¬0¶, s(κ) = λ implies that o(κ) ≥ λ in the core model.