godelTheoremsCert
plain-language theorem explainer
This definition supplies a certified record asserting exactly five limitative results on formal systems. Researchers examining structural incompleteness or its embedding in Recognition Science would cite it for the fixed count matching configuration dimension 5. The construction assembles the record by direct assignment from the pre-proven cardinality theorem.
Claim. The structure requiring that the cardinality of the set of limitative results equals 5 is instantiated by assigning its sole field to the established count of 5, where the set comprises Gödel's first and second incompleteness theorems, Tarski's undefinability of truth, Church's undecidability of the Entscheidungsproblem, and Turing's halting problem.
background
The module groups Gödel's two incompleteness theorems with Tarski's undefinability, Church's undecidability, and Turing's halting problem as five distinct limits on formal systems, corresponding to configuration dimension D = 5. The referenced structure encodes the requirement that the finite type cardinality of these results equals 5. An upstream theorem establishes this equality by decision procedure, with the module reporting zero sorries and zero axioms.
proof idea
The definition constructs the certificate instance by setting the five_results field directly to the value of the cardinality theorem.
why it matters
This definition completes the structural certification of the five limitative results, aligning with the module's grouping that matches configDim D = 5. It supplies a clean reference point for the Recognition Science treatment of incompleteness without further scaffolding. The module doc emphasizes the zero-axiom status, providing a fixed count for any downstream embedding of these limits.
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