# 2003 seminar talk: Around Sheva-Sheva-Sheva: forcing for the lambda-reals (where lambda is inaccessible)

Talk held by Andrzej Roslanowski (University of Nebraska at Omaha) at the KGRC seminar on 2003-05-27.

### Abstract

A number of cardinal characteristics related to the Baire space, the Cantor space and/or the combinatorial structure of [omega]^omega can be extended to the spaces obtained by replacing omega by lambda (for any infinite cardinal lambda). Following the tradition of Set Theory of the Reals we may call cardinal numbers defined this way "cardinal characteristics of lambda-reals". The menagerie of those characteristics seems to be much larger than the one for the continuum, but to decide if the various definitions lead to different (and interesting) cardinals we need a well developed forcing technology. We will present initial steps in this direction. This is a joint work with Saharon Shelah.