3 papers
math.LO1999
The number of L_{infty,kappa}-equivalent non-isomorphic models for kappa weakly compact
Saharon Shelah, Pauli Väisänen
For a cardinal kappa and a model M of cardinality kappa let No(M) denote the number of non-isomorphic models of cardinality kappa which are L_{infty,kappa}--equivalent to M. In [Sh…
math.LO1999
On equivalence relations Sigma_1^1-definable over H(kappa)
Saharon Shelah, Pauli Väisänen
Let kappa be an uncountable regular cardinal. Call an equivalence relation on functions from kappa into 2 Sigma_1^1-definable over H(kappa) if there is a first order sentence F and…
math.LO1999
On the number of L_{infty,omega_1}-equivalent non-isomorphic models
Saharon Shelah, Pauli Vaisanen
We prove that if ZF is consistent then ZFC+GCH is consistent with the following statement: There is for every k<omega a model of cardinality aleph_1 which is L_{infty,omega_1}-equi…