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- W1820365790 abstract "Sets may be considered to be simpler than functions. This chapter proposes an axiomatic theory with a fundamental epsilon-like notion E . The stronger theory of enumeration of functions is also developed in the chapter. Besides the relation E some other individual constants or functions (primitive recursive in the standard model) as primitive notions are also required. The shifting function S allowing considering some elements as combinators with respect to the equivalence is introduced in the chapter. The chapter introduces a fixed point theorem stating that there is a function π which produces fixed points. It also discusses non-extensionality theorem, which states that “for every element x and for every n there exist more than n elements which are extensional with x ." @default.
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- W1820365790 date "1974-01-01" @default.
- W1820365790 modified "2023-09-27" @default.
- W1820365790 title "Axiomatic Theory of Enumeration" @default.
- W1820365790 doi "https://doi.org/10.1016/s0049-237x(08)70597-4" @default.
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