We are proving the following: (1) If κ is a weakly inaccessible then NSκ is not κ -saturated. (2) If κ is a weakly inaccessible and θ < κ is regular then NS κ is not κ saturated. (3) If κ is singular then NS κ+ is not κ-saturated. Combining this with previous results of Shelah, one obtains the following: (A) If κ > א1 then NSκ is not κ -saturated. (B) If θ < κ then NS κ is not κ -saturated.

Fe–30Mn–10.5Al–1.1C alloys with different Mo and Ni contents are prepared to investigate the phase transformation behavior mechanical properties of austenitic lightweight steels. Solution-treated samples have microstructures consisting an austenite matrix ordered κ-carbides, size κ-carbides decreases addition or Ni. In addition, body-centered cubic (BCC) phases B2 DO3 also form when 3wt%Mo 3wt%...

Definition 0.1 Let δ be a cardinal. We say that δ is Woodin with 3 iff there is some sequence (a κ : κ < δ) such that a κ ⊂ V κ for every κ < δ and for every A ⊂ V δ the set {κ < δ : A ∩ V κ = a κ ∧ κ is A–strong up to δ} is stationary in δ. Proof. Let us define ((a κ , c κ) : κ < δ) recursively as follows. If ((a κ , c κ) : κ < µ) is defined for some µ < δ, then we let (a µ , c µ) be the least...

κ-Karaginan adalah koloid hidrofilik yang diekstrak dari makroalga Eucheuma cottonii. κ-karaginan mempunyai berat molekul sangat besar sehingga pemanfaatannya terbatas. Namun, dalam bentuk Carrageenan Oligosaccharide (COs), aktivitas fisik dan biologi bervariasi, termasuk anti tumor, oksidan angiogenik. Enzim κ-karaginase berperan memutus ikatan β-(1,4) pada untuk menghasilkan κ-COs (κ-carragee...

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+.

We prove that, in any fine structural extender model with Jensen’s λ-indexing, there is a (κ)-sequence if and only if there is a pair of stationary subsets of κ ∩ cof(< κ) without common reflection point of cofinality < κ which, in turn, is equivalent to the existence of a family of size < κ of stationary subsets of κ ∩ cof(< κ) without common reflection point of cofinality < κ. By a result of ...

We generalize ∇(A), which was introduced in [2], to larger cardinals. For a regular cardinal κ > א0 we denote by ∇κ(A) the statement that A ⊂ κ and for all regular θ > κ do we have that {X ∈ [Lθ[A]] <κ : X ∩ κ ∈ κ ∧ otp(X ∩ OR) ∈ Card} is stationary in [Lθ[A]] . It was shown in [2] that ∇א1(A) can hold in a set-generic extension of L. We here prove that ∇א2(A) can hold in a semi-proper set-gene...

the κ-casein protein plays a fundamental role in milk production and its composition synthesis in the mammary gland. this protein has an important role in the formation, stabilization, and aggregation of the casein micelles. in this study, we investigated the genetic variability at the exon 4 of the κ-casein gene (also known as csn3) using pcr-sscp analysis and dna sequencing. then a protein se...