Robinson arithmetic is a weak finitely axiomatized first-order theory sufficient for numeralwise representation of computable finite calculations and the diagonal lemma. Its extensions are sufficiently strong for the soundness-based incompleteness argument.
Robinson arithmetic, denoted as \( R \), is a weak system of arithmetic that is part of the field of mathematical logic and foundational studies. It was introduced by the mathematician and logician John Robinson in the 1950s. The key features of Robinson arithmetic include: 1. **Language**: The language of Robinson arithmetic includes a number of basic symbols for logical operations (like conjunction and disjunction), equality, and a unary function symbol typically interpreted as a successor function.
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