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On infinite series of infinite isols

Published online by Cambridge University Press:  12 March 2014

Joseph Barback
Joseph Barback*
Affiliation:
Department of Mathematics, State University of New York College at Buffalo, Buffalo, New York 14222
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Extract

We are interested in regressive isols, recursive functions, and the extensions of recursive functions to the isols. One of the nicest concepts that has been applied to the study of these notions is of an infinite series of isols. J. C. E. Dekker introduced infinite series of isols in [3]. With this concept one may associate with each number theoretic function u and regressive isol B a value in the isols to correspond to the series

When u is chosen as a recursive function, or as a recursive combinatorial function, many of the sums that one associates with familiar finite series may be generalized to infinite series. For example, if B is any regressive isol, then

The results presented in our paper were motivated by an interest in extending infinite series to a setting where the terms being summed may be infinite isols. In our paper, we do this in a special way, as will be described below. We would first like to briefly comment on some facts about the concept of defining an infinite series in the isols.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 2 , June 1988 , pp. 443 - 462
Copyright
Copyright © Association for Symbolic Logic 1988

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References

REFERENCES

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