Geodesic
On decidability of the theory $\mathrm{Th}(\omega,0,1,,+,f_0,\dots,f_n)$
Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 3, pp. 72-90.

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In the paper we consider theories which are obtained from the Semenov arithmetics introducing functions $f_i$, $i>0$. They are called “hyperfunctions” and they are obtained when we iterate an addition-connected function. We have proved, that such theories are model complete. It is also shown, that these theories are decidable when the condition of effective periodicity is satisfied for hyperfunctions.
Keywords: Semenov arithmetic, hyperfunction, Ackermann function. 
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A. S. Snyatkov. On decidability of the theory $\mathrm{Th}(\omega,0,1,<,+,f_0,\dots,f_n)$. Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 3, pp. 72-90. http://geodesic.mathdoc.fr/item/MAIS_2010_17_3_a5/

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