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.

We provide a model where u(κ) < 2κ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that...

We prove the following: Theorem A. If D is a (λ+, κ)-regular ultrafilter, then either (a) D is (λ, κ)-regular, or (b) the cofinality of the linear order ∏ D〈λ, <〉 is cf κ, and D is (λ, κ′)-regular for all κ′ < κ. Corollary B. Suppose that κ is singular, κ > λ and either λ is regular, or cf κ < cf λ. Then every (λ+n, κ)-regular ultrafilter is (λ, κ)-regular. We also discuss some consequences and...

Given a topological groupG (usually compact abelian), the authors study the poset D = D(G) of dense subgroups of G and its impact on the algebraic structure of G. A key tool for this is the subgroup den(G) := ∩ D. Definition. For a cardinal κ ≥ 1, a topological group is in the class Ff (κ) [F(κ); F2(κ); Fad(κ), respectively] if some family of κ-many dense subgroups of G is independent and freel...

If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ-strategically closed forcing and λ is weakly compact, then we show that A = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets} must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to cons...

We present the main features of the mathematical theory generated by the κ-deformed exponential function expκ(x) = ( √ 1 + κ2x2 + κx), with 0 ≤ κ < 1, developed in the last twelve years, which turns out to be a continuous one parameter deformation of the ordinary mathematics generated by the Euler exponential function. The κ-mathematics has its roots in special relativity and furnishes the theo...