Contents: (Math. Log. Quart. 1–2/2013)
Mathematical logic quarterly · 2013
Complexity and Expressive Power of Second-Order Extended Horn LogicWe introduce SO-HORN r which is a revised version of SO-HORN and show that SO-HORN r captures P on ordered finite structures.We also introduce second-order Extended Horn logic SO-EHORN and a superclass SO-EHORN r of it.We show that both of them capture co-NP on ordered finite structures by proving that SO-EHORN and SO-EHORN r have the same expressive power when only consider ordered structures. Page 12-18Eric Jaligot Two remarks on elementary theories of groups obtained by free constructionsWe give two slight generalizations of results of Poizat about elementary theories of groups obtained by free constructions.The first-one concerns generic types and the non-superstability of such groups in many cases.The second-one concerns the connectedness of most free products of groups without amalgamation.