On Axiomatizability of the Multiplicative Theory of Numbers
نویسنده
چکیده
The multiplicative theory of a set of numbers is the theory of the structure of that set with (solely) the multiplication operation (that set is taken to be multiplicative, i.e., closed under multiplication). In this paper we study the multiplicative theories of the complex, real and (positive) rational numbers. These theories are known to be decidable; here we present some explicit axiomatizations for them and show that they are not finitely axiomatizable. For each of these sets (of complex, real and rational numbers) a language, including the multiplication operation, is introduced in a way that it allows quantifier elimination (for the theory of that set).
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ورودعنوان ژورنال:
- Fundam. Inform.
دوره 159 شماره
صفحات -
تاریخ انتشار 2018