A Solution to a Problem of Marek and Truszcyński

We first show that every normal default theory is representable in the class of free normal default theories. This gives a new feature of extensions of normal default theories. By the above result an example of default theory is obtained which is not reprsentable in the class of normal default theories but has exactly infinitely countably many extensions and those extensions are pairwisely inconsistent. It gives a solution to a problem of W. Marek and M. Truszcyński and refutes a related assertion presented by them.