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… 
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