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Separation principles in the hierarchy theory of pure first-order logic1

Published online by Cambridge University Press:  12 March 2014

M. R. Krom
M. R. Krom*
Affiliation:
University of California, Davis
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Extract

This paper answers negatively the chief remaining open questions concerning the separation properties of first-order prefix classes of structures (discussed by Addison [2], pp. 26–37).

1. Preliminaries. The first and second separation properties and the reduction property are defined for arbitrary classes of subsets of an arbitrary set.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 3 , September 1963 , pp. 222 - 236
Copyright
Copyright © Association for Symbolic Logic 1964

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Footnotes

1

This paper is from the author's doctoral dissertation which was written at the University of Michigan.

References

[1]Addison, J. W., Separation principles in the hierarchies of classical and effective set theory, Fundamenta Mathematicae, vol. 46 (1959), pp. 123–135.CrossRefGoogle Scholar
[2]Addison, J. W., The theory of hierarchies, Logic, methodology and philosophy of science, Proceedings of the 1960 international congress, Stanford University Press, Palo Alto 1962, pp. 26–37.Google Scholar
[3]Addison, J. W., Some problems in hierarchy theory, Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, American mathematical society, vol. 5, (1962), pp. 123–130.CrossRefGoogle Scholar
[4]Craig, W., Linear reasoning. A new form of the Herbrand-Gentzen theorem, this Journal, vol. 22 (1957), pp. 250–268.Google Scholar
[5]Kleene, S. C., Introduction to metamathematics, D. Van Nostrana Company, New York and Toronto 1952.Google Scholar
[6]Tarski, A. and Vaught, R., Arithmetical extensions of relational systems, Compositio Mathematica, vol. 13 (1957), pp. 84–102.Google Scholar