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Deciding whether a relation defined in Presburger logic can be defined in weaker logics. (English) Zbl 1158.03007
The author defines a structure 2 to be decidable in a structure 1 (for 1 , 2 on the same domain and such that each basic relation of 2 is definable in 1 ) if it is decidable for a relation first-order definable in 1 whether it is first-order definable in 2 . For 1 being Presburger arithmetic (both on and ), he shows that all 2 built taking at least two of the three types of basic relations (xc), (x-yc) and (x=b mod a) are decidable in Presburger arithmetic.
03B25Decidability of theories; sets of sentences
03B10First-order logic
03D05Automata theory in connection with logical questions
68Q45Formal languages and automata