Online research in philosophy

We prove the hereditary undecidability of the L t theories of: (1) torsion-free Hausdorff topological abelian groups; (2) locally pure Hausdorff topological abelian groups.

THEOREM. The Jacobson radical of an ℵ 0 -categorical associative ring is nilpotent.

Orthogonality between two stably embedded definable sets is preserved under the addition of constants.

The problem of the existence of a universal structure omitting a finite set of forbidden substructures is reducible to the corresponding problem in the category of graphs with a vertex coloring by two colors. It is not known whether this problem reduces further to the category of ordinary graphs. It is also not known whether these problems are decidable.

We analyze the two cardinal properties of definable sets in homogeneous graphs.

We show that all QE rings of prime power characteristic are constructed in a straightforward way out of three components: a filtered Boolean power of a finite field, a nilpotent Jacobson radical, and the ring Z p n or the Witt ring W 2 (F 4 ) (which is the characteristic four analogue of the Galois field with four elements).

oris, 1986, 17-34, Seminarberichte 86, Humboldt University, Berlin, where, with G. Cherlin, we gave a detailed proof of a result of Alexei L. Semenov that the theory of (N, +, 2x) is decidable and admits quantifier elimination in an expansion of the language containing the Presburger..