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. 
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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/

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