Core models

Abstract

The following rough summary is intended to give the non-specialist in fine-structure an idea of what core models are and what they are used for. References are usually given to proofs but very few proofs are given. Also attribution of results is rather careless: I hope to give full historical notes in a forthcoming more detailed exposition.Jensen is certainly responsible for the bulk of these results. This paper is based in part on a lecture he gave in Oxford in 1979, and my warmest thanks are due to him for his patient explanations of these results. (I should add that he has not seen this paper in proof and should not be held responsible for any false claims which it contains.) Mitchell has been the main driving force behind the generalisations of K, and his influence on the results in §5 is perhaps not adequately reflected there. The language of “hypermeasures” has been replaced here by “extenders”, but the reader of [14] will find translation easy.Graeme Forbes, Robin Gandy, Wilfrid Hodges and the referee read the paper in proof and I am most grateful for their many suggested improvements.