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Model. Anal. Inform. Sist., 2010, Volume 17, Number 3, Pages 72–90 (Mi mais25)  

On decidability of the theory $\mathrm{Th}(\omega,0,1,<,+,f_0,…,f_n)$

A. S. Snyatkov

Tver State University

Abstract: 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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UDC: 510.65
Received: 18.05.2010

Citation: A. S. Snyatkov, “On decidability of the theory $\mathrm{Th}(\omega,0,1,<,+,f_0,…,f_n)$”, Model. Anal. Inform. Sist., 17:3 (2010), 72–90

Citation in format AMSBIB
\Bibitem{Sny10}
\by A.~S.~Snyatkov
\paper On decidability of the theory $\mathrm{Th}(\omega,0,1,<,+,f_0,\dots,f_n)$
\jour Model. Anal. Inform. Sist.
\yr 2010
\vol 17
\issue 3
\pages 72--90
\mathnet{http://mi.mathnet.ru/mais25}
\elib{http://elibrary.ru/item.asp?id=15237186}


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