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We have published several articles about generalizations and boundary-caseexceptions to the Second Incompleteness Theorem during the last 25 years. Thecurrent paper will review some of our prior results and also introduce an`enriched' refinement of semantic tableaux deduction. While the SecondIncompleteness Theorem is a strong result, we will emphasize its boundary-caseexceptions are germane to Global Warming's threat because our systems can own asimultaneous knowledge about their own consistency, together with anunderstanding of the $\Pi_1$ implications of Peano Arithmetic.

About the Chasm Separating the Goals of Hilbert's Consistency Program from the Second Incompletess Theorem