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- W2246358954 abstract "Let WO$(omega^omega)$ be the statement that the ordinal number $omega^omega$ is well ordered. WO$(omega^omega)$ has occurred several times in the reverse-mathematical literature. The purpose of this expository note is to discuss the place of WO$(omega^omega)$ within the standard hierarchy of subsystems of second-order arithmetic. We prove that WO$(omega^omega)$ is implied by I$Sigma^0_2$ and independent of B$Sigma^0_2$. We also prove that WO$(omega^omega)$ and B$Sigma^0_2$ together do not imply I$Sigma^0_2$." @default.
- W2246358954 created "2016-06-24" @default.
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- W2246358954 date "2015-08-11" @default.
- W2246358954 modified "2023-09-27" @default.
- W2246358954 title "Comparing WO$(omega^omega)$ with $Sigma^0_2$ induction" @default.
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