PARIS-HARRINGTON
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Large Cardinals and PH
n=6 · k=3-subsets · 2 colors
SCENARIO
While PH needs only a little beyond PA (just ε₀), large cardinal axioms yield Ramsey-type principles vastly stronger.
RAMSEY CONTEXT
The large cardinal hierarchy produces an infinite ladder of increasingly strong Ramsey-type statements.
PA ANALYSIS
Measurable cardinals imply partition relations for infinite cardinals — the 'completed infinity' version of Ramsey theory.
PH is just the first step on a staircase of independent combinatorial principles, each requiring more axiomatic strength.
True but unprovable in PA · ε₀ boundary · rotates daily