Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T14:21:56.703Z Has data issue: false hasContentIssue false

The combinatorics of combinatorial coding by a real

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Affiliation:
Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel, E-mail: [email protected] Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, E-mail: [email protected]
Lee J. Stanley
Affiliation:
Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015, E-mail: [email protected]

Abstract

We lay the combinatorial foundations for [5] by setting up and proving the essential properties of the coding apparatus for singular cardinals. We also prove another result concerning the coding apparatus for inaccessible cardinals.

Type
Research Article
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 Notes Series, vol. 47, Cambridge University Press, Cambridge, 1982.CrossRefGoogle Scholar
[2]Donder, H.-D., Jensen, R., and Stanley, L., Condensation-coherent global square systems, Recursion theory, Proceedings of Symposia in Pure Mathematics, vol. 42, (Nerode, A. and Shore, R., editors), American Mathematical Society, Providence, Rhode Island, 1985, pp. 237259.CrossRefGoogle Scholar
[3]Jensen, R., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229308.CrossRefGoogle Scholar
[4]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., editors), Springer-Verlag, Berlin, 1992, pp. 407416.CrossRefGoogle Scholar
[5]Shelah, S. and Stanley, L., A combinatorial forcing for coding the universe by a real when there are no sharps, this Journal, vol. 60 (1994), pp. 135.Google Scholar