Geodesic
Generic Kleene fixed point theorem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 732-736

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Kleene's fixed point theorem states that any algorithmic mapping $\mathcal{A}$ of the set of Turing machines to the set of Turing machines has a fixed point: there is a Turing machine $M$ such that machine $\mathcal{A}(M)$ computes the same function as $M$. In this paper we prove a generic analog of this theorem: any algorithmic mapping $\mathcal{A}$ of a set of “almost all” Turing machines to the set of Turing machines has a fixed point.
Keywords: Kleene fixed point theorem, generic computability. 
@article{SEMR_2017_14_a20,
     author = {A. N. Rybalov},
     title = {Generic {Kleene} fixed point theorem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {732--736},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a20/}
}
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A. N. Rybalov. Generic Kleene fixed point theorem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 732-736. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a20/