Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-12T22:30:20.538Z Has data issue: false hasContentIssue false
  • English
  • Français

Predicate calculus with free quantifier variables1

Published online by Cambridge University Press:  12 March 2014

Richmond H. Thomason  and
D. Randolph Johnson Jr
Richmond H. Thomason
Affiliation:
Yale University
D. Randolph Johnson Jr
Affiliation:
Yale University
Get access Rights & Permissions [Opens in a new window]

Extract

In the literature of symbolic logic there are many examples of systems having free variables ranging over truth-values, individuals, or predicates. But, though many such systems are equipped with universal and existential quantifiers (and though many other quantifiers, e.g., for exactly one, are thereby definable), the problem of free variables corresponding to such constants has been neglected.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 1 , 29 May 1969 , pp. 1 - 7
Copyright
Copyright © Association for Symbolic Logic 1969

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.)

Footnotes

1

The research resulting in this paper was sponsored by the National Science Foundation, under grant GS-1567. The authors wish to thank the referee for his helpful suggestions.

References

[1]Fuhrken, G., Languages with added quantifier “there exist at least ℵa”, The theory of models, edited by Addison, J., Henkin, L., and Tarski, A., North-Holland, Amsterdam, 1965, pp. 121–131.Google Scholar
[2]Henkin, L., The completeness of the first-order functional calculus, this Journal, vol. 14 (1949), pp. 159–166.Google Scholar
[3]Henkin, L., Completeness in the theory of types, this Journal, vol. 15 (1950), pp. 81–91.Google Scholar
[4]Mostowski, A., On a generalization of quantifiers, Fundamenta mathematicae, vol. 44 (1957), pp. 12–36.CrossRefGoogle Scholar
[5]Tarski, A., Der Wahrheitsbegriff in den formalisierten Sprachen, Studia philosophica, vol. 1 (1936), pp. 261–405.Google Scholar
[6]Thomason, R., A system of logic with free variables ranging over quantifiers (abstract), this Journal, vol. 31 (1966), p. 700.Google Scholar
[7]Yasuhara, M., Incompleteness of Lp languages, Fundamenta mathematicae (to appear).Google Scholar