Contents: (Math. Log. Quart. 3/2018)
Mathematical logic quarterly · 2018
On elimination of quantifiers in some non-classical mathematical theories Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds.Furthermore, it is suggested that only by moving to more extensional underlying logics can we get the property back.Page 155-169 Quentin Brouette and Franc ¸oise Point On differential Galois groups of strongly normal extensionsWe revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed.In certain classes of differential topological fields, which encompasses ordered or p-valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general.In the class of ordered differential fields, using elimination of imaginaries in CODF, we establish a relative Galois correspondence for relatively definable subgroups of the group of differential order automorphisms.