Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T02:29:42.335Z Has data issue: false hasContentIssue false
  • English
  • Français

Core models

Published online by Cambridge University Press:  12 March 2014

A.J. Dodd
A.J. Dodd*
Affiliation:
Merton College, Oxford, England
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 1 , March 1983 , pp. 78 - 90
Copyright
Copyright © Association for Symbolic Logic 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Cohen, P. J., The independence of the continuum hypothesis, Proceedings of the National Academy of Science of the United States of America, vol. 50 (1963), pp. 1143–1148; vol. 51 (1964), pp. 105–110.CrossRefGoogle ScholarPubMed
[2]Devlin, K. J. and Jensen, R. B., Marginalia to a theorem of Silver, ISILC Logic Conference, Lecture Notes in Mathematics, no. 499, Springer-Verlag, Berlin and New York, 1975 pp. 115–142.Google Scholar
[3]Dodd, A. J. and Jensen, R. B., The core model, Annals of Mathematical Logic, vol. 20 (1981), pp. 43–75.CrossRefGoogle Scholar
[4]Dodd, A. J., The covering lemma for K, Annals of Mathemical Logic (to appear).Google Scholar
[5]Dodd, A. J., Mice based on extenders, handwritten notes.Google Scholar
[6]Dodd, A. J., Superstrong cardinals, handwritten notes.Google Scholar
[7]Easton, W. B., Powers of regular cardinals, Annals of Mathematical Logic, vol. 1 (1970), pp. 139–178.CrossRefGoogle Scholar
[8]Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[9]Jensen, R. B., Application of K/embeddings of K, handwritten notes.Google Scholar
[10]Jensen, R. B., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308.CrossRefGoogle Scholar
[11]Magidor, M., On the singular cardinals problem, Israel Journal of Mathematics, vol. 28 (1977), pp. 1–31 and Annals of Mathematics, vol. 106 (1977), pp. 514–547.CrossRefGoogle Scholar
[12]Mitchell, William J., Sets constructible from sequences of ultrafilters, this Journal, vol. 39 (1974), pp. 57–66.Google Scholar
[13]Mitchell, William J., Ramsey cardinals and constructibility, this Journal, vol. 44 (1979), pp. 260–266.Google Scholar
[14]Mitchell, William J., Hypermeasurable cardinals, Logic colloquium 1978 (Boffa, M.et al., Editors), North-Holland, Amsterdam, 1979, pp. 303–316.Google Scholar
[15]Scott, D. S., Measurable cardinals and constructible sets, Bulletin de l'Académic Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques vol. 9 (1961), pp. 521–524.Google Scholar
[16]Silver, J. H., Some applications of model theory in set theory, Annals of Mathematical Logic, vol. 3 (1971), pp. 45–110.CrossRefGoogle Scholar
[17]Silver, J. H., On the singular cardinals problem, Proceedings of the International Congress of Mathematicians, Vancouver, 1974, pp. 265–268.Google Scholar
[18]Solovay, R. M., A fine structure theory for LD, handwritten notes.Google Scholar
[19]Welch, P., D. Phil, thesis, Oxford, 1979.Google Scholar