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  "body": "\n## Summary\n\nRobinson arithmetic, often written $\\mathsf{Q}$, is a first-order theory of the natural numbers with zero, successor, addition and multiplication.\nIt has seven axioms and no induction.\nIt is much weaker than the [[Peano axioms|0QFT7Z76N5]], yet strong enough to represent every computable function.\nFor this reason the incompleteness theorems and many undecidability results already hold for $\\mathsf{Q}$ and every consistent theory that extends it.\n\n## Explanations\n\n### L1 human\n\nRobinson arithmetic keeps only the recursive rules for addition and multiplication and a few facts about successor.\nIt can check any particular computation, such as $2 + 2 = 4$.\nBut without induction it cannot prove general laws such as $x + y = y + x$.\nIts value is that it is a small, finite list of axioms that still captures all of computation.\n",
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