Genre: Information/Explanation

Buy & download fulltext article: Given a class of structures K and n ??, we study the dichotomy between there being countably many n -back-and-forth equivalence classes and there being continuum many. In the latter case, we show that, relative to some oracle, every set can be weakly coded in the ( n -1)st jump of some structure in K. In the former case, we show that there is a countable set of infinitary ? n relations that captures all of the ? n information about the structures in K. In most cases, where there are countably many n -back-and-forth equivalence classes, there is a computable description of them. We will show how to use this computable description to get a complete set of computably infinitary ? n formulas. This will allow us to completely characterize the relatively intrinsically ? n +1 0 relations in the computable structures of K, and to prove that no Turing degree can be coded by the ( n -1)st jump of any structure in K unless that degree is already below 0( n -1). The Journal of Logic and Computation aims to promote the growth of logic and computing, including, among others, the following areas of interest: Logical Systems, such as classical and non-classical logic, constructive logic, categorical logic, modal logic, type theory, feasible maths.... Logical issues in logic programming, knowledge-based systems and automated reasoning; logical issues in knowledge representation, such as non-monotonic reasoning and systems of knowledge and belief; logics and semantics of programming; specification and verification of programs and systems; applications of logic in hardware and VLSI, natural language, cincurrent computation, planning, and databases. The bulk of the content is technical scientific papers, although letters, reviews, and discussions, as well as relevant conference reviews, are included.