Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-24T17:36:22.372Z Has data issue: false hasContentIssue false
  • English
  • Français

A combinatorial forcing for coding the universe by a real when there are no sharps

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah  and
Lee J. Stanley
Saharon Shelah
Affiliation:
The Hebrew University of Jerusalem, Department of Mathematics, Jerusalem, Israel, E-mail: shelah@sunrise.huji.ac.il Rutgers University, Department of Mathematics, New Brunswick, New Jersey 08903, E-mail: shelah@math.rutgers.edu
Lee J. Stanley
Affiliation:
Lehigh University, Department of Mathematics, Bethlehem, PA 18015, E-mail: ljs4@lehigh.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Assuming 0# does not exist, we present a combinatorial approach to Jensen's method of coding by a real. The forcing uses combinatorial consequences of fine structure (including the Covering Lemma, in various guises), but makes no direct appeal to fine structure itself.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 1 , March 1995 , pp. 1 - 35
Copyright
Copyright © Association for Symbolic Logic 1995

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]Beller, A., Jensen, R., and Welch, P., Coding the universe, London Mathematical Society Lecture Note Series, vol. 47, Cambridge University Press, Cambridge, 1982.CrossRefGoogle Scholar
[2]David, R., Some applications of Jensen's coding theorem, Annals of Mathematical Logic, vol. 22 (1982), pp. 177–196.CrossRefGoogle Scholar
[3]David, R., reals, Annals of Pure and Applied Logic, vol. 23 (1982), pp. 121–125.Google Scholar
[4]David, R., A functorial singleton, Advances in Mathematics, vol. 74 (1989), pp. 258–268.CrossRefGoogle Scholar
[5]Friedman, S., A guide to ‘Coding the universe’ by Beller, Jensen, Welch, this Journal, vol. 50 (1985), pp. 1002–1019.Google Scholar
[6]Friedman, S., An immune partition of the ordinals, Recursion theory week; proceedings Oberwolfach 1984, Lecture Notes in Mathematics, vol 1121, (Ebbinghaus, H.-D., et al., editors), Springer-Verlag, Berlin, 1985, pp. 141–147.Google Scholar
[7]Friedman, S., Strong coding, Annals of Pure and Applied Logic, vol. 35 (1987), pp. 1–98, 99–122.CrossRefGoogle Scholar
[8]Friedman, S., Coding over a measurable cardinal, this Journal, vol. 54 (1989), pp. 1145–1159.Google Scholar
[9]Friedman, S., Minimal coding, Annals of Pure and Applied Logic, vol. 41 (1989), pp. 233–297.CrossRefGoogle Scholar
[10]Friedman, S., The -singleton conjecture, Journal of the American Mathematical Society, vol. 3 (1990), pp. 771–791.Google Scholar
[11]Friedman, S., A simpler proof of Jensen's coding theorem, Annals of Pure and Applied Logic (to appear).Google Scholar
[12]Friedman, S., A large Π set, absolute for set forcings, Proceedings of the American Mathematical Society, vol. 122 (1994), pp. 253–256.Google Scholar
[13]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol 940, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[14]Shelah, S., Cardinal arithmetic, Oxford University Press, Oxford (to appear).CrossRefGoogle Scholar
[15]Shelah, S. and Stanley, L., Corrigendum to ‘Generalized Martin's axiom and Souslin's hypothesis for higher cardinals’, Israel Journal of Mathematics, vol. 53 (1986), pp. 304–314.CrossRefGoogle Scholar
[16]Shelah, S. and Stanley, L., Coding and reshaping when there are no sharps, Set theory of the continuum, Mathematical Sciences Research Institute Publications, vol. 26 (Judah, H., et al.), Springer-Verlag, Berlin, 1992, pp. 407–416.CrossRefGoogle Scholar
[17]Shelah, S. and Stanley, L., The combinatorics of combinatorial coding by a real, this Journal, vol. 60 (1994), pp. 36–57.Google Scholar