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The Journal of Symbolic Logic The Journal of Symbolic Logic

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The combinatorics of combinatorial coding by a real

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah  and
Lee J. Stanley
Saharon Shelah
Affiliation:
Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel, E-mail: shelah@sunrise.huji.ac.il Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, E-mail: shelah@math.rutgers.edu
Lee J. Stanley
Affiliation:
Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015, E-mail: ljs4@lehigh.edu
Corresponding
E-mail address:
shelah@sunrise.huji.ac.il
shelah@math.rutgers.edu
ljs4@lehigh.edu
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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
Information
The Journal of Symbolic Logic , Volume 60 , Issue 1 , March 1995 , pp. 36 - 57
Copyright
Copyright © Association for Symbolic Logic 1995

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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. 237–259.CrossRefGoogle Scholar
[3]Jensen, R., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308.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. 407–416.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. 1–35.Google Scholar

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