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Our earlier publications showed semantic tableau admits partial exceptions tothe Second Incompleteness Theorem where a formalism recognizes its selfconsistency and views multiplication as a 3-way relation (rather than as atotal function). We now show these boundary-case evasions will collapse if theLaw of the Excluded Middle is treated by tableau as a schema of logical axioms(instead of as derived theorems).

How the Law of Excluded Middle Pertains to the Second Incompleteness Theorem and its Boundary-Case Exceptions