The equivalence of definable quantifiers in second order arithmetic
The isomorphism relation between tree-automatic Structures
An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that...
The smallest common extension of a sequence of models of ZFC
In this note, we show that the model obtained by finite support iteration of a sequence of generic extensions of models of ZFC of length is sometimes the smallest common extension of this sequence and very often it is not.