Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-25T19:44:19.575Z Has data issue: false hasContentIssue false
  • English
  • Français

The metamathematics of model theory: Discovering language in action

Published online by Cambridge University Press:  12 March 2014

Douglas E. Miller
Douglas E. Miller*
Affiliation:
University of Illinois at Chicago, Circle, Chicago, Illinois 60680
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss the problem of defining the collection of first-order elementary classes in terms of the natural topological space of countable models.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 3 , September 1981 , pp. 490 - 498
Copyright
Copyright © Association for Symbolic Logic 1981

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]Bourbaki, N., General topology. Part 2, Addision-Wesley, New York, 1966.Google Scholar
[2]Burgess, J. P., Two selection theorems, Bulletin de la Société Mathématique de Grèce, vol. 18 (1977), pp. 121–126.Google Scholar
[3]Craig, W., Boolean notions extended to higher dimensions, The theory of models (Addison, , Henkin, , Tarski, , Editors), North-Holland, Amsterdam, 1972.Google Scholar
[4]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[5]Gurevich, Y., Monadic theory of order and topology 1, Israel Journal of Mathematics, vol. 27(1977), pp. 299–319.CrossRefGoogle Scholar
[6]Keisler, H. J., Finite approximations to infinitely long formulas, The theory of models, op. cit.Google Scholar
[7]Kuratowski, K., Les types d'ordre définissables et les ensembles boréliens, Fundamenta Mathematicae, vol. 28 (1937), pp. 97–100.CrossRefGoogle Scholar
[8]Lopez-Escobar, E. G. K., An interpolation theorem for denumerably long formulas, Fundamenta Mathematicae, vol. 57 (1965), pp. 253–272.CrossRefGoogle Scholar
[9]Miller, D. E., The invariant Πα0 separation principle, Transactions of the American Mathematical Society, vol. 242 (1978), pp. 185–204.Google Scholar
[10]Miller, D. E., An application of invariant sets to global definability, this Journal, vol. 44 (1979) pp. 9–14.Google Scholar
[11]Scott, D., Logic with denumerably long formulas and finite strings of quantifiers, Theory of models, op. cit.Google Scholar
[12]Shoenfield, J., Mathematical logic, Addison-Wesley, New York, 1967.Google Scholar
[13]Vaught, R. L., Invariant sets in topology and logic, Fundamenta Mathematicae, vol. 82 (1974), pp. 269–294.CrossRefGoogle Scholar