The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It led to the prediction and the observation of physical phenomena which confirm the important role of general relativity in physics. The understanding of the do...

We consider edge colourings of the complete r-uniform hypergraph K (r) n on n vertices. How many colours may such a colouring have if we restrict the number of colours locally? The local restriction is formulated as follows: for a fixed hypergraph H and an integer k we call a colouring (H, k)-local if every copy of H in the complete hypergraph K (r) n receives at most k different colours. We in...

Abstract We show that there is no theory minimal with respect to interpretability among recursively enumerable essentially undecidable theories.