How one would explain to layman what does it mean if the elementary theory of some algebraic structure is decidable? I guess it has something to do with halting of Turing machines.
2026-03-25 10:52:13.1774435933
What does it mean that an elementary theory is decidable?
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It means that there is some systematic procedure (indeed, think computation or algorithm) that can take any expression that the theory is about and that correctly decides whether that statement is part of the theory (i.e. true) or not. And yes, this decision needs to be reached at some point, i.e. the algorithm needs to halt at some point and give its correct verdict.