Accumulation functions on the ordinals
Artur Rubin, Jean Rubin (1971)
Fundamenta Mathematicae
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Artur Rubin, Jean Rubin (1971)
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An epsilon number is a transfinite number which is a fixed point of an exponential map: ωϵ = ϵ. The formalization of the concept is done with use of the tetration of ordinals (Knuth's arrow notation, ↑). Namely, the ordinal indexing of epsilon numbers is defined as follows: [...] and for limit ordinal λ: [...] Tetration stabilizes at ω: [...] Every ordinal number α can be uniquely written as [...] where κ is a natural number, n1, n2, …, nk are positive integers, and β1 > β2 > …...
P. Knight (1972)
Fundamenta Mathematicae
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