Geodesic
The computational power of infinite time Blum–Shub–Smale machines
Algebra i logika, Tome 56 (2017) no. 1, pp. 55-92

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Functions that are computable on infinite time Blum–Shub–Smale machines (ITBM) are characterized via iterated Turing jumps, and we propose a normal form for these functions. It is also proved that the set of ITBM computable reals coincides with $\mathbb R\cap L_{\omega^\omega}$.
Keywords: infinite time Blum–Shub–Smale machines, infinite computations, iterated jump, ITBM, BSS-machines, computable reals. 
@article{AL_2017_56_1_a2,
     author = {P. Koepke and A. S. Morozov},
     title = {The computational power of infinite time {Blum{\textendash}Shub{\textendash}Smale} machines},
     journal = {Algebra i logika},
     pages = {55--92},
     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_1_a2/}
}
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P. Koepke; A. S. Morozov. The computational power of infinite time Blum–Shub–Smale machines. Algebra i logika, Tome 56 (2017) no. 1, pp. 55-92. http://geodesic.mathdoc.fr/item/AL_2017_56_1_a2/