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...

We say that κ is μ-hypermeasurable (or μ-strong) for a cardinal μ ≥ κ+ if there is an embedding j : V → M with critical point κ such that H(μ)V is included in M and j(κ) > μ. Such j is called a witnessing embedding. Building on the results in [7], we will show that if V satisfies GCH and F is an Easton function from the regular cardinals into cardinals satisfying some mild restrictions, then th...

statement of problem: dental caries is one of the common diseases in the world. it is an infective disease which is caused by loss of minerals and destruction of dental tissues. one of the most effective ways to diagnose the interproximal caries is radiography. bitewing radiography is the best way for caries diagnosis. purpose: the aim of this study was to evaluate the prevalence of the interpr...

ion. LEQ-λ Γ, X :pκ ` F ≤ F ′ : κ′ Γ ` λXF ≤ λXF ′ : pκ→ κ′ Application. There are two kinds of congruence rules for application: one kind states that if functions F and F ′ are in the subtyping relation, so are their values F G and F ′G at a certain argument G. LEQ-FUN Γ ` F ≤ F ′ : pκ→ κ′ p−1Γ ` G : κ Γ ` F G ≤ F ′G : κ′ The other kind of rules concern the opposite case: If F is a function an...