Invariant subsets of scattered trees. An application to the tree alternative property of Bonato and Tardif

A tree is scattered if no subdivision of the complete binary tree is a subtree. Building on results of Halin, Polat and Sabidussi, we identify four types of subtrees of a scattered tree and a function of the tree into the integers at least one of which is preserved by every embedding. With this result and a result of Tyomkyn, we prove that the tree alternative property conjecture of Bonato and Tardif holds for scattered trees and a conjecture of Tyomkin holds for locally finite scattered trees

Models with second order properties, V: A General principle

We present a general framework for carrying out some constructions. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which would be much easier in a generic extension of the universe, and the second player cheats with the aid of Diamond. Section 1 contains an axiomatic framework suitable for the description of a number of related constructions, and the statement of the main theorem in terms of this framework. In section 2 we illustrate the use of our combinatorial principle. The proof of the main result is then carried out in sections 3-5

Inflation des diplômes et insertion professionnelle des jeunes : situation des diplômés du secondaire professionnel et du cégep technique sur le marché de l’emploi

Le discours officiel soutient que les jeunes ont besoin de formation pour s'insérer dans le marché de l'emploi. Pendant que la population en général s'instruit de plus en plus et que des modèles théoriques expliquent le rôle de la formation dans l'insertion professionnelle, la situation des jeunes sur le marché de l'emploi ne cesse de se dégrader. Ce texte examine la valeur, sur le marché de l'emploi, du diplôme des finissants du secondaire et du collégial, et pose la question du rapport entre le système d'enseignement et le système de production.The official discourse supports the idea that young people need training in order to enter the job market. However, while the general population shows increases in the level of education and various theoretical models explain the importance of training in entering professional fields, the situation for young people searching to enter the job market is deteriorating. This article examines the value accorded to a diploma for high school and college graduates and further questions the relation between the instructional system and the production system.El discurso oficial sostiene que los jovenes tienen necesidad de formacion para insertarse dentro del mercado de trabajo. Mientras la poblacion se instruye cada vez mas y los modelos teoricos explican el roi de la formacion dentro de la insercion profesional, la situacion de los jovenes en el mercado de trabajo no cesa de degradarse. Este texto examina el valor que tiene en el mercado de trabajo, el diploma de secundaria y colegial y cuestiona la relacion que existe entre el sistema de ensenanza y el sistema productivo.Der offizielle Diskurs unterstûtzt den Bildungsbedarf von Jugendlichen, der dazu behilflich ist, sich im Arbeitsmarkt einzufûgen. Wâhrend die Bevôlkerung zunehmend an Bildung gewinnt und Theoriemodelle erlâutern, wie wichtig Bildung zur Einfugung ins Berufsleben ist, verschlechtert sich dennoch zunehmend die Lage fur Jugendliche auf dem Arbeitsmarkt. Dieser Text untersucht, wieviel Giiltigkeit ein AbschlufSzeugnis der Real-und Gymnasialstufe auf dem Arbeitsmarkt besitzt. Ferner wird die Beziehung zwischen Lehr-und Produktionssystem untersucht

Pairs of orthogonal countable ordinals

We characterize pairs of orthogonal countable ordinals. Two ordinals $\alpha$ and $\beta$ are orthogonal if there are two linear orders $A$ and $B$ on the same set $V$ with order types $\alpha$ and $\beta$ respectively such that the only maps preserving both orders are the constant maps and the identity map. We prove that if $\alpha$ and $\beta$ are two countable ordinals, with $\alpha \leq \beta$, then $\alpha$ and $\beta$ are orthogonal if and only if either $\omega + 1\leq \alpha$ or $\alpha =\omega$ and $\beta < \omega \beta$