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Dear Dwohnitmok, 1: Model theory, which formalizes "truth", is very important for understanding inferential incompleteness. Axioms of found
by ProfHewitt 6y ago
Dear Dwohnitmok,
1: Model theory, which formalizes "truth", is very
important for understanding inferential
incompleteness. Axioms of foundational theories of
Computer Science have just *one* model up to a unique
isomorphism, which defines "truth".
The theorems of foundational theories of Computer
Science are *not* computationally enumerable.
Consequently, even the provable proposition's
*cannot* be computationally enumerated, much less the
ones true in the unique model.
2. Foundational theories of Computer Science can prove
their own consistency because they *disallow* the
[Gödel 1931] proposition *I'mUnprovable*, which if it
were allowed would make the theories inconsistent.