ABSTRACT Nadia Boulanger and Her Role in Polish Music – the Light of Zygmunt Mycielski–s Writings Mycielski (1907–1987), a composer writer on music, was one pupils (1887–1979). In his writings he often stressed role which this eminent French teacher played development whole generation (and not only Polish) composers. Not did owe lot to her personally, but also clearly saw significance teaching ...

The local chromatic number of a graph, introduced by Erdős et al. in [3], is the minimum number of colors that must appear in the closed neighborhood of some vertex in any proper coloring of the graph. This talk, based on the papers [13, 14, 15], would like to survey some of our recent results on this parameter. We give a lower bound for the local chromatic number in terms of the lower bound of...

The local chromatic number of a graph G is the number of colors appearing in the most colorful closed neighborhood of a vertex minimized over all proper colorings of G. We show that two specific topological obstructions that have the same implications for the chromatic number have different implications for the local chromatic number. These two obstructions can be formulated in terms of the hom...

We show that the Ehrenfeucht-Mycielski sequence U is strongly balanced in the following sense: for any finite word w of length k, the limiting frequency of w in U is 2. 1. The Ehrenfeucht-Mycielski Sequence In [2] Ehrenfeucht and Mycielski introduced an infinite binary word based on avoiding repetitions. More precisely, to construct the Ehrenfeucht-Mycielski (EM) sequence U , start with a singl...

This paper concerns the classification of finite coloured linear orders up to n-equivalence. Ehrenfeucht-Fräıssé games are used to define what this means, and also to help analyze such structures. We give an explicit bound for the least number g(m, n) such that any finite m-coloured linear order is n-equivalent to some ordering of size ≤ g(m, n), from which it follows that g is computable. We g...

The authors show, by means of a finitary version fin λ,D of the combinatorial principle b ∗ λ of [6], the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ, if Mi and Ni are elementarily equivalent models of a language of size ≤ λ, then the second player has a winning strategy in the Ehrenfeucht-Fräıssé...

Motivated by Leibniz’s thesis on the identity of indiscernibles, Mycielski introduced a set theoretic axiom, here dubbed the Leibniz-Mycielski axiom LM, which asserts that for each pair of distinct sets x and y there exists an ordinal α exceeding the ranks of x and y, and a formula φ(v), such that (V α ,∈) satisfies φ(x) ∧ ¬φ(y) . We examine the relationship between LM and some other axioms of ...