Post's Problem in Constructive Mathematics
Abstract
Our proof reveals that as only non-constructive logical principle it suffices to assume (¬¬Σ1)-LEM, stating that for any Σ1 set A, ¬¬∀x. x ∈ A ∨ x ̸ ∈ A. In usual settings of constructive reverse mathematics, this principle is classified as strictly weaker than LEM, LPO, or even ¬¬LPO.
Our proof is explained in (analytic) textbook computability theory based on a model of computation, but additionally formally backed by a machine-checked development in synthetic computability using the Rocq proof assistant.
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