Abelian p-groups with no invariants

AbstractWe prove for abelian p-groups a non-structure theorem relative to approximations of Ehrenfeucht-Fraïssé games of length ω1 in terms of linear orderings with no uncountable descending sequences. Our result shows that there is a group which is too complicated to be characterized up to isomorphism by the Ehrenfeucht-Fraïssé game approximated by a fixed ordering. This means that such a group cannot have any complete invariants which are bounded in the sense of these approximations of the Ehrenfeucht-Fraïssé game. On the other hand, all the approximations characterize together the notion of isomorphism among groups of cardinality at most ω1. From the point of view of Stability Theory, our result concerns certain stable theories with NDOP and NOTOP

The three worlds and two sides of mathematics and a visual construction for a continuous nowhere differentiable function

Peer reviewe

Instructors’ views on the developmental needs of peer tutoring in the non-formal learning environment

There is a need to organize non-formal learning activities in mathematics for children and youth. In Finland, we are developing a new non-formal learning environment called Pulmaario where we use peer tutors as instructors. This study is the empirical problem analysis of the design-based research. The aim was to find out what kind of support the instructors of the Pulmaario learning environment felt they need. The research material (N=51) was collected with questionnaires. The analysis of the questionnaires was based on the method of inductive content analysis. The results shows the needs for developing the non-formal learning environment further.Non peer reviewe