Let κ be a regular uncountable cardinal and λ ≥ κ. The principle of stationary reflection for Pκλ has been successful in settling problems of infinite combinatorics in the case κ = ω1. For a greater κ the principle is known to fail at some λ. This note shows that it fails at every λ if κ is the successor of a regular uncountable cardinal or κ is countably closed.

The purpose of this note is to describe a framework which unifies radial, chordal and dipolar SLE. When the definition of SLE(κ; ρ) is extended to the setting where the force points can be in the interior of the domain, radial SLE(κ) becomes chordal SLE(κ; ρ), with ρ = κ− 6, and vice versa. We also write down the martingales describing the Radon–Nykodim derivative of SLE(κ; ρ1, . . . , ρn) with...

Given a supercompact cardinal κ and a regular cardinal λ < κ, we describe a type of forcing such that in the generic extension the cofinality of κ is λ, there is a very good scale at κ, a bad scale at κ, and SCH at κ fails. When creating our model we have great freedom in assigning the value of 2, and so we can make SCH hold or fail arbitrarily

We introduce an extension, indexed by a partially ordered set P and cardinal numbers κ, λ, denoted by (κ,<λ) ; P , of the classical relation (κ, n, λ) → ρ in infinite combinatorics. By definition, (κ, n, λ) → ρ holds if every map F : [κ] → [κ] has a ρ-element free set. For example, Kuratowski’s Free Set Theorem states that (κ, n, λ) → n + 1 holds iff κ ≥ λ+n, where λ+n denotes the n-th cardinal...

Given an uncountable regular cardinal κ, a partial order is κstationarily layered if the collection of regular suborders of P of cardinality less than κ is stationary in Pκ(P). We show that weak compactness can be characterized by this property of partial orders by proving that an uncountable regular cardinal κ is weakly compact if and only if every partial order satisfying the κ-chain conditio...

Starting from a supercompact cardinal κ, we build a model, in which κ is singular string limit, the singular cardinal hypothesis fails at κ and there are no very good scales at κ. Moreover there is a bad scale at κ, and so weak square fails.

Object of the present paper is to study pseudo Hermitian magnetic curves in (κ,µ) manifold admitting Zamkovoy connection. We give main classification theorem for pseudo-Hermitian curve. Again we find curvature and torsion a (κ,µ)-manifold

κ-carbide hardening in a ferrite-austenite duplex low-density FeMnAlC steel has been investigated as a function of annealing processing within the temperature range 500−900 o C. Below 600 o C, a high hardness can be attained by the fine microstructures, e.g. the thin lamellar κ-carbides in austenite and dispersed nanosized particulate κ-carbides in ferrite. After further annealing, the alloy so...

We explore two possible generalizations of the Euler formula for the complex κ-exponential, which give two different sets of κ-deformed cyclic functions endowed with different analytical properties. In a case, the κ-sine and κ-cosine functions take real values on R and are characterized by an asymptotic log-periodic behavior. In the other case, the κ-cyclic functions take real values only in th...