Formal theories of arithmetic

Skolem arithmetic

In mathematical logic, Skolem arithmetic is the first-order theory of the natural numbers with multiplication, named in honor of Thoralf Skolem. The signature of Skolem arithmetic contains only the multiplication operation and equality, omitting the addition operation entirely. Skolem arithmetic is weaker than Peano arithmetic, which includes both addition and multiplication operations. Unlike Peano arithmetic, Skolem arithmetic is a decidable theory. This means it is possible to effectively determine, for any sentence in the language of Skolem arithmetic, whether that sentence is provable from the axioms of Skolem arithmetic. The asymptotic running-time computational complexity of this decision problem is triply exponential. (Wikipedia).

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Related pages

Quantifier elimination | Decision problem | Ehrenfeucht–Fraïssé game | Greatest common divisor | Robinson arithmetic | Presburger arithmetic | Decidability (logic) | Multiplication | Multiset | Natural number | Fundamental theorem of arithmetic | NP (complexity) | Prime number | Least common multiple | Mathematical logic | Feferman–Vaught theorem | Computational complexity theory | Satisfiability | Equinumerosity | Thoralf Skolem | First-order logic