# 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} }

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…

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