1154 Jakob Kellner And

Creature forcing and five cardinal characteristics in Cichoń's diagram

A Sacks real out of nowhere

There is a proper countable support iteration of length ω adding no new reals at finite stages and adding a Sacks real in the limit.

Winning the pressing down game but not Banach-Mazur

Let S be the set of those α ∈ ω2 that have cofinality ω1. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length ω1, but not the Banach Mazur game of length ω+1 (both games starting with S).

F–Products and Nonstandard Hulls for Strongly Continuous One–parameter Semigroups of Linear Operators

We give an overview of the F–product construction and the corresponding nonstandard constructions and show that (in the case of bounded ultrapowers) both constructs are isomorphic (theorem 3.15). From this we also follow a little “classical” corollary (3.14). The nonstandard construction has been investigated in [Wol84] and [Wol], the corresponding classical constructions first appeared in [Der...

F-products and nonstandard hulls for semigroups

Derndinger [Der80] and Krupa [Kru90] defined the F–product of a (strongly continuous one–parameter) semigroup (of linear operators) and presented some applications (e.g. to spectral theory of positive operators, cf. [EN00]). Wolff (in [Wol84] and [Wol00]) investigated some kind of nonstandard analogon and applied it to spectral theory of group representations. The question arises in which way t...