Geodesic
The index set of linear orderings that are autostable relative to strong constructivizations
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 3, pp. 51-60

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We prove that a computable ordinal $\alpha$ is autostable relative to strong constructivizations if and only if $\alpha\omega^{\omega+1}$. We calculate, in a precise way, the complexity of the index set for linear orderings that are autostable relative to strong constructivizations.
Keywords: computable model, strongly constructivizable model, autostability, autostability relative to strong constructivizations, linear ordering, computable ordinal, index set. 
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     author = {S. S. Goncharov and N. A. Bazhenov and M. I. Marchuk},
     title = {The index set of linear orderings that are autostable relative to strong constructivizations},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
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     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2015_15_3_a4/}
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S. S. Goncharov; N. A. Bazhenov; M. I. Marchuk. The index set of linear orderings that are autostable relative to strong constructivizations. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 3, pp. 51-60. http://geodesic.mathdoc.fr/item/VNGU_2015_15_3_a4/