Presburgerness of predicates regular in two number systems. (English) Zbl 0411.03054


03F30 First-order arithmetic and fragments
03B25 Decidability of theories and sets of sentences
03B10 Classical first-order logic
03D05 Automata and formal grammars in connection with logical questions


Zbl 0369.02023
Full Text: DOI


[1] A. L. Semenov, ?Presburgerness of sets recognizable by finite automata in two number systems,? Third All-Union Conference of Mathematical Logic. Reports Abstracts [in Russian], Izd. Inst. Math. Sib. Otdel. Akad. Nauk SSSR, Novosibirsk (1974), pp. 201-203.
[2] J. R. Büchi, ?Weak second-order arithmetic and finite automata,? Z. Math. Logik Grundl. Math.,6, No. 1, 66-92 (1960); Kiberneticheskii Sb., No. 8, 42-77 (1964). · Zbl 0103.24705
[3] A. Cobham, ?On the base-dependence of sets of numbers, recognizable by finite automata,? Math. Systems Theory,3, No. 2, 186-192 (1969); Kiberneticheskii Sb., Nov. Ser., No. 8, 62-71 (1971). · Zbl 0179.02501
[4] S. Ginsburg and E. H. Spanier, ?Semigroups, Presburger formulas and languages,? Pac. J. Math.,13, No. 4, 570-581 (1966). · Zbl 0143.01602
[5] J. W. Thatcher, ?Decision problems for multiple successor arithmetics,? J. Symbolic Logic,31, No. 2, 182-190 (1966). · Zbl 0144.00106
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