Abstract
Two arithmetic constructive theories based on Dialectica interpretation are introduced and studied in the paper. For an arithmetic formula A let AD be its Dialectica interpretation in the language of arithmetic in all finite types. The translation (AD)° of AD back into the language of first-order arithmetic using the system HRO of hereditary recursive operations is considered. The theories T1 and T2 consist of arithmetic sentences A such that (AD)° is true in the standard model and provable in the intuitionistic arithmetic respectively. Using the author's recent results on the arithmetic complexity of the predicate logics of constructive arithmetic theories it is proved that the logic of T1 is not recursively enumerable and the logic of T2 is II2-complete.
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