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The two-cardinal problem for languages of arbitrary cardinality

Published online by Cambridge University Press:  12 March 2014

Luis Miguel
Affiliation:
Departamento de Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, 09340 D.F., México. E-mail: lmvs@xanum.uam.mx
Villegas Silva
Affiliation:
Departamento de Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, 09340 D.F., México. E-mail: lmvs@xanum.uam.mx

Abstract

Let ℒ be a first-order language of cardinality κ++ with a distinguished unary predicate symbol U. In this paper we prove, working on L, the two cardinal transfer theorem (κ+,κ) ⇒ (κ++, κ+) for this language. This problem was posed by Chang and Keisler more than twenty years ago.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2010

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References

REFERENCES

[Chang65]Chang, C. C., A note on the two-cardinal problem, Proceedings of the American Mathematical Society, vol. 16 (1965), pp. 11481155.CrossRefGoogle Scholar
[CK93]Chang, C. C. and Keisler, H. J., Model theory, 3rd ed., North-Holland, 1993.Google Scholar
[Dev84]Devlin, K., Constructibility, Springer-Verlag, 1984.CrossRefGoogle Scholar
[Don81]Donder, H. D., Coarse morasses in L, Lecture Notes in Mathematics, vol. 872, Springer-Verlag, 1981.Google Scholar
[Hod93]Hodges, W., Model theory, Cambridge Univerisy Press, 1993.CrossRefGoogle Scholar
[Jen72]Jensen, R. B., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229308.CrossRefGoogle Scholar
[JenKar]Jensen, R. B. and Karp, C., Primitive recursive set functions, Axiomatic set theory (Scott, D., editor), Proceedings of Symposia in Pure Mathematics, vol. 13, American Mathematical Society, 1971, pp. 143167.CrossRefGoogle Scholar
[Jen1]Jensen, R. B., Morasses I, (unpublished manuscript).Google Scholar
[Jen2]Jensen, R. B., C-morasses, (unpublished manuscript).Google Scholar
[KenSh02]Kennedy, J. and Shelah, S., On regular reduced products, this Journal, vol. 67 (2002), pp. 11691177.Google Scholar
[Vill06]Villegas-Silva, L. M., A gap-1 transfer theorem, Mathematical Logic Quarterly, vol. 52 (2006), no. 4, pp. 340350.CrossRefGoogle Scholar