Forcing Arguments in Second-Order Arithmetic - Google Sites

Forcing Arguments in Second-Order Arithmetic Kenji Omoto Tohoku University

2012/2/20

Reverse Mathematics I

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Setting: Second order arithmetic.

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Main Question: What axioms are necessary to prove the theorems of Mathematics?

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Axiom systems(Big 5): RCA0 ≡ ∆11 -Comprehension + Σ01 -Induction + Semiring ax WKL0 ≡ RCA0 + Weak K¨onig’s lemma ACA0 ≡ RCA0 + Arithmetic Comprehension ATR0 1 Π1 -CA0

≡ ACA0 + Arithmetic Transfinite recursion ≡ ACA0 + Π11 -Comprehension

Theories of Second-Order Arithmetic I ▶

∪ A set is called arithmetical ( n