A universal space is one that continuously maps onto all others of its own kind and weight. We investigate when a universal Uniform Eberlein compact space exists for weight κ. If κ = 2<κ, then they exist whereas otherwise, in many cases including κ = ω1, it is consistent that they do not exist. This answers (for many κ and consistently for all κ) a question of Benyamini, Rudin and Wage of 1977.

Starting from the κ-distribution function, obtained by applying the maximal entropy principle to the κ-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical κ-partition function and discuss its main properties. It is shown that all important macroscopical quantities of the system can be expressed employing only the κ-partition function. The relations...

Let T be a complete, first-order theory in a finite or countable language having infinite models. Let I(T, κ) be the number of isomorphism types of models of T of cardinality κ. We denote by μ (respectively μ̂) the number of cardinals (respectively infinite cardinals) less than or equal to κ. Theorem I(T, κ), as a function of κ > א0, is the minimum of 2 κ and one of the following functions: 1. 2...

We show that a strong form of the so called Lindström’s Theorem [4] fails to generalize to extensions of Lκω and Lκκ : For weakly compact κ there is no strongest extension of Lκω with the (κ, κ)-compactness property and the Löwenheim-Skolem theorem down to κ . With an additional set-theoretic assumption, there is no strongest extension of Lκκ with the (κ, κ)-compactness property and the Löwenhe...

Plasma shaping effects on temperature gradient-driven instabilities and geodesic acoustic oscillations are investigated with a gyrokinetic theory and a local magnetohydrodynamics equilibrium model. In specific, we focus on the effect of the elongation κ , including its radial derivative ( )( ) r r s ∂ ∂ = κ κ κ , in the large aspect ratio limit. An analytical formula of the dependence of the GA...

Objectives. To assess interreader agreements and a learning curve between three (senior, junior, and beginner) different experienced musculoskeletal ultrasonographers. Senior served as the imaging "gold standard". Methods. Clinically dominant joints (finger, shoulder, knee, tibiotalar, and talonavicular) of 15 rheumatoid arthritis (RA) patients were examined by three different experienced ultra...

For I a proper, countably complete ideal on P(X) for some set X , can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski [Si] in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal κ, and that I is a κ-complete ideal on P(κ) containing all singletons. In this paper we provide consequences from ...

The full duality between the κ-Poincaré algebra and κ-Poincaré group is proved.

We deal with the problem of preserving various versions of completeness in (< κ)–support iterations of forcing notions, generalizing the case " S–complete proper is preserved by CS iterations for a stationary co-stationary S ⊆ ω 1 ". We give applications to Uniformization and the Whitehead problem. In particular, for a strongly inaccessible cardinal κ and a stationary set S ⊆ κ with fat complem...

A model (M,!,...) is κ-like if M has cardinality κ but, for all a `M, the cardinality of 2x `M : x! a ́ is strictly less than κ. In this paper we shall give constructions of κ-like models of arithmetic satisfying an arbitrarily large finite part of PA but not PA itself, for various singular cardinals κ. The main results are : (1) for each countable nonstandard MzΠ # ®Th(PA) with arbitrarily larg...