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- W1836700871 abstract "The famous Godel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being added as axioms, but where can we obtain them? One classical (and well studied) approach is to add (to some theory T) an axiom that claims the consistency of T. In this note we discuss the other one (motivated by Chaitin's version of the Godel theorem) and show that it is not really useful (in the sense that it does not help us to prove new interesting theorems), at least if we are not limiting the proof complexity. We discuss also some related questions." @default.
- W1836700871 created "2016-06-24" @default.
- W1836700871 creator A5083603294 @default.
- W1836700871 date "2011-09-26" @default.
- W1836700871 modified "2023-09-26" @default.
- W1836700871 title "Are random axioms useful?" @default.
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- W1836700871 doi "https://doi.org/10.48550/arxiv.1109.5526" @default.
- W1836700871 hasPublicationYear "2011" @default.
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