Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-18T07:51:00.535Z Has data issue: false hasContentIssue false
  • English
  • Français

The two-cardinal problem for languages of arbitrary cardinality

Published online by Cambridge University Press:  12 March 2014

Luis Miguel  and
Villegas Silva
Luis Miguel
Affiliation:
Departamento de Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, 09340 D.F., México. E-mail: [email protected]
Villegas Silva
Affiliation:
Departamento de Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, 09340 D.F., México. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Coarse morasscardinal transfer theoremtwo-cardinal problem
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010 , pp. 785 - 801
Copyright
Copyright © Association for Symbolic Logic 2010

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

[Chang65]Chang, C. C., A note on the two-cardinal problem, Proceedings of the American Mathematical Society, vol. 16 (1965), pp. 1148–1155.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. 229–308.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. 143–167.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. 1169–1177.Google Scholar
[Vill06]Villegas-Silva, L. M., A gap-1 transfer theorem, Mathematical Logic Quarterly, vol. 52 (2006), no. 4, pp. 340–350.CrossRefGoogle Scholar