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- W1025722046 abstract "This chapter provides the formalization of the theory of ordinal diagrams of infinite order. There is a discussion about a formal theory of some systems of ordinal diagrams, which have been used to prove the consistency of subsystems of classical analysis. By exhibiting a formal system in which the consistency proofs can be formalized, Gödel's incompleteness theorem can be used (in the form that no system can prove its own consistency) to form an estimate of what the limits are of the power of such methods. The chapter presents a formal system that is constructive. The intuitionistic arithmetic, that is, Peano's axioms plus primitive recursive definitions plus the intuitionistic predicate calculus are described. The properties of primitive recursive functions can be used and predicates freely in terms of mathematical axioms." @default.
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- W1025722046 date "1970-01-01" @default.
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- W1025722046 title "Formalization of the Theory of Ordinal Diagrams of Infinite Order" @default.
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- W1025722046 doi "https://doi.org/10.1016/s0049-237x(08)70764-x" @default.
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