CRT²₂ implies exponential closure of I⁰₁ over RCA₀* (with proof speedup and unprovability consequences), while SRT²₂ is polynomially simulated by RCA₀* for ∀Π⁰₃ sentences but implies quasipolynomial closure of I⁰₁.
Ramsey’s theorem for pairs, collection, and proof size.J
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The cohesive and stable Ramsey theorems and proof size over a weak base theory
CRT²₂ implies exponential closure of I⁰₁ over RCA₀* (with proof speedup and unprovability consequences), while SRT²₂ is polynomially simulated by RCA₀* for ∀Π⁰₃ sentences but implies quasipolynomial closure of I⁰₁.