Measure theory and weak König's lemma
Archive for Mathematical Logic 30 (3):171-180 (1990)
Abstract
We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive on open setsDOI
10.1007/bf01621469
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References found in this work
Which set existence axioms are needed to prove the cauchy/peano theorem for ordinary differential equations?Stephen G. Simpson - 1984 - Journal of Symbolic Logic 49 (3):783-802.
Which set existence axioms are needed to prove the separable Hahn-Banach theorem?Douglas K. Brown & Stephen G. Simpson - 1986 - Annals of Pure and Applied Logic 31:123-144.
Π10 classes and Boolean combinations of recursively enumerable sets.Carl G. Jockusch - 1974 - Journal of Symbolic Logic 39 (1):95-96.
