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Definability and decision problems in arithmetic

Published online by Cambridge University Press:  12 March 2014

Julia Robinson
Julia Robinson*
Affiliation:
University of California
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Extract

In this paper, we are concerned with the arithmetical definability of certain notions of integers and rationals in terms of other notions. The results derived will be applied to obtain a negative solution of corresponding decision problems.

In Section 1, we show that addition of positive integers can be defined arithmetically in terms of multiplication and the unary operation of successor S (where Sa = a + 1). Also, it is shown that both addition and multiplication can be defined arithmetically in terms of successor and the relation of divisibility | (where x|y means x divides y).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 14 , Issue 2 , 23 June 1949 , pp. 98 - 114
Copyright
Copyright © Association for Symbolic Logic 1949

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References

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