Strong subgroup chains and the Baer-Specker group

Examples are given of non-elementary properties that are preserved under C-filtrations for various classes C of Abelian groups. The Baer-Specker group is never the union of a chain of proper subgroups with cotorsionfree quotients. Cotorsion-free groups form an abstract elementary class (AEC). The Kaplansky invariants of the Baer-Specker group are used to determine the AECs defined by the perps of the Baer-Specker quotient groups that are obtained by factoring the Baer-Specker group B of a ZFC extension by the Baer-Specker group A of the ground model, under various hypotheses, yielding information about its stability spectrum.Comment: 12 page

A result related to the problem CN of Fremlin

We show that the set of injective functions from any uncountable cardinal less than the continuum into the real numbers is of second category in the box product topology

On modules which are self-slender

This paper is an examination of the dual of the fundamental isomorphism relating homomorphism groups involving direct sums and direct products over arbitrary index sets. We prove that for every cardinal μ, with μ ℵ0 = μ, there exists a non-slender self-slender self-small group of cardinality μ+

LABORARTORY BRNO

Studie galerie architektury, moderního umění a designu na rušné křižovatce dvou velmi důležitých brněnských ulic. Poznávání klasické úlohy navrhování nárožní budovy.Study of an architecture, contemporary art and design gallery at busy intersection of two very important streets in Brno. Exploring classical problem of a corner site building design.

Říká logicismus něco, co se říkat nemá?

The objective of this paper is to analyze the broader significance of Frege’s logicist project against the background of Wittgenstein’s philosophy from both Tractatus and Philosophical Investigations. The article draws on two basic observations, namely that Frege’s project aims at saying something that was only implicit in everyday arithmetical practice, as the so-called recursion theorem demonstrates, and that the explicitness involved in logicism does not concern the arithmetical operations themselves, but rather the way they are defined. It thus represents the attempt to make explicit not the rules alone, but rather the rules governing their following, i.e. rules of second-order type. I elaborate on these remarks with short references to Brandom’s refinement of Frege’s expressivist and Wittgenstein’s pragmatist project