# Definability and Decision Problems in Arithmetic

```@article{Robinson1949DefinabilityAD,
title={Definability and Decision Problems in Arithmetic},
author={Julia Jean Robinson},
journal={J. Symb. Log.},
year={1949},
volume={14},
pages={98-114}
}```
• J. Robinson
• Published 1 June 1949
• Mathematics, Computer Science
• J. Symb. Log.
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…
314 Citations

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