Consider the structure $(\mathbb{N};\times,S,0,1)$, where $\times$ represents multiplication and $S$ represents successor. Is the addition function definable by a first-order formula in that structure? That is, is there a first order formula with three free variables $x,y,z$ such that the formula holds iff $x+y=z$?
2026-03-29 07:30:03.1774769403
Is addition definable from successor and multiplication?
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