On Decidability of the Theory <i>Th(u, 0,1,<, +, f</i>_<i></i>_<i>0</i><i></i><i>,..., f</i>_<i></i>_<i>n</i><i></i><i>)</i>

Abstract

In the paper we consider theories which are obtained from the Semenov arithmetics introducing functions fi,i > 0. They are called "hyperfuncctions" and they are obtained when we iterate an addition-connexctexd function. We have provexl, that such theories are model complete. It is also shown, that these theories are dexidable when the condition of eSexctive periodicity is satis&exd for hyperfuncctions.

Keywords

• арифметика семенова
• гиперфункция
• функция аккермана