Abstract
The logic \(\mathcal{L}\)(T) of an arbitrary first order theory T is the set of predicate formulas provable in T under every interpretation into the language of T. We prove that if T is an arithmetically correct theory in the language of arithmetic, or T is the theory of fields, the theory of rings, or an inessential extension of the theory of groups, then \(\mathcal{L}\)(T) coincides with the predicate calculus PC. We also study inclusion relations and decidability for the logics of Presburger's arithmetic of addition, Skolem's arithmetic of multiplication and other decidable theories.
The research described in this publication was made possible in part by the Russian Foundation for Basic Research (project 96-01-01395).
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Yavorsky, R.E. (1997). Logical schemes for first order theories. In: Adian, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 1997. Lecture Notes in Computer Science, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63045-7_41
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DOI: https://doi.org/10.1007/3-540-63045-7_41
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