Erratum for: A study of homogeneity in relational databases [Annals of Mathematics and Artificial Intelligence 33(2) (2001) 379-414]

摘要

In definition 3.5 in [3], where we define the class QCQ~k, for every k ≥ 1, we need to add a second requirement for a query to be in the class QCQ~k, namely that the answer to every query f in the class QCQ~k is always the union of complete FO~k types. Previously, we considered that property to be implied by our definition, but it turns out that it is not so. There are total computable queries which for some k ≥ 1 preserve realization of FO~k types for k-tuples, but whose evaluation on some databases defines a relation which has not complete FO~k types for k-tuples. One example of such queries is the query which defines a total order in the class of Odd Multipedes of Gurevich and Shellah. We give below the correct definition, which should replace definition 3.5 in [3].