Lucrările Simpozionului Internaţional Cartea, România, Europa. Ediţia a II-1, 20–24 septembrie 2009. Edited by Julieta Rotaru. Secţiunea a treia: Studii Euroasiatice şi Afroasiatice—De la mit la ritual. Bucharest: Editura Biblioteca Bucureştilor, 2010. Pp. 461–738. Travaux de Symposium International Le Livre, la Roumanie, l’Europe. Troisième édition, 20–24 septembre 2010. Vol. 3: Études euro- et afro-asiatiques, III A: La Veda-Vedāṅga et l’Avesta entre oralité et écriture. Edited by Jan E. M. Houben and Julieta Rotaru. Bucharest: Éditeur Bibliothèque de Bucarest, 2011. Pp. (...) 11–532. (shrink)

We show that the first order theory of the lattice $\mathscr{L}^{ (S) of finite dimensional closed subsets of any nontrivial infinite dimensional Steinitz Exhange System S has logical complexity at least that of first order number theory and that the first order theory of the lattice L(S ∞ ) of computably enumerable closed subsets of any nontrivial infinite dimensional computable Steinitz Exchange System S ∞ has logical complexity exactly that of first order number theory. Thus, for example, the lattice of (...) finite dimensional subspaces of a standard copy of $\bigoplus_\omega$ Q interprets first order arithmetic and is therefore as complicated as possible. In particular, our results show that the first order theories of the lattice L(V ∞ ) of c.e. subspaces of a fully effective ℵ 0 -dimensional vector space V∞ and the lattice of c.e. algebraically closed subfields of a fully effective algebraically closed field F ∞ of countably infinite transcendence degree each have logical complexity that of first order number theory. (shrink)

Purpose: My goals in this paper are to comment on some of the roles that Ernst von Glasersfeld played in our work in IRON (Interdisciplinary Research on Number) from circa 1975 up until the time of his death, and to relate certain events that revealed his character in very human terms. Method: Among my recollections of Ernst, I have chosen those that I felt would most adequately portray his impact on the field of mathematics education and his ethics in the (...) field of human affairs. Findings: It has not often been said but, in his work in IRON, it was Ernst’s explicit intention to start a conceptual revolution in mathematics education and beyond. Other than serving as a revolutionary, Ernst also served as a mentor for many investigators in mathematics education, including myself. He excelled as a scientist as well an epistemologist, and his scientific work fueled his epistemological work. Ernst was a very ethical and wonderful human being who was dedicated to the betterment of humankind by means of his revolutionary ideas. (shrink)

This collection of articles pays homage to the creativity and scientific rigor Jerome Singer has brought to the study of consciousness and play. It will interest personality, social, clinical and developmental psychologists alike.

Philosophical Studies Vol. 2, No. 2, p. 163, l. 24 for ‘Pocreon’ read “Creon’ and p. 165, l.4 for “Nereus” read “Nessus”, l. 16 for “Corrolate” read “Correlate” and l. 27 for “ Trachinae ” read “ Trachiniae ”. Proffessor Mackinnon should also have been described as Norris-Hulse Professor of Divinity in the University of Cambridge and Fellow of Corpus Christi College.