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• W2973179377 abstract "Abstract We investigate the strength of a randomness notion ${cal R}$ as a set-existence principle in second-order arithmetic: for each Z there is an X that is ${cal R}$ -random relative to Z . We show that the equivalence between 2-randomness and being infinitely often C -incompressible is provable in $RC{A_0}$ . We verify that $RC{A_0}$ proves the basic implications among randomness notions: 2-random $Rightarrow$ weakly 2-random $Rightarrow$ Martin-Löf random $Rightarrow$ computably random $Rightarrow$ Schnorr random. Also, over $RC{A_0}$ the existence of computable randoms is equivalent to the existence of Schnorr randoms. We show that the existence of balanced randoms is equivalent to the existence of Martin-Löf randoms, and we describe a sense in which this result is nearly optimal." @default.
• W2973179377 created "2019-09-19" @default.
• W2973179377 creator A5047690936 @default.
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• W2973179377 date "2019-09-09" @default.
• W2973179377 modified "2023-10-18" @default.
• W2973179377 title "RANDOMNESS NOTIONS AND REVERSE MATHEMATICS" @default.
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• W2973179377 doi "https://doi.org/10.1017/jsl.2019.50" @default.
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