Geodesic
On Sums of Computable Ordinals
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 2, pp. 3-8

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It was proved, that for any computable ordinal $\alpha$ there are notation $a \in O$ and partially computable function with propery: for two notations $b$ and $c$ from set $\{ t \in O \mid t $ for ordinals $\beta$ and $\gamma$, $\beta + \gamma \alpha$, it can find notation for $\beta + \gamma$ from this set. And we show, that not all notations for ordinals $\alpha \geqslant \omega^{2}$ has this property.
Keywords: computable ordinal, notation for computable ordinals, computable function. 
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     author = {P. E. Alaev},
     title = {On {Sums} of {Computable} {Ordinals}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
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     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_2_a0/}
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P. E. Alaev. On Sums of Computable Ordinals. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 2, pp. 3-8. http://geodesic.mathdoc.fr/item/VNGU_2014_14_2_a0/