The Arithmetic Hierarchy, Parikh’s Theorem and Related Matters
نویسنده
چکیده
1 The Arithmetic Hierarchy Our language or signature is 〈+, ·, <, 0, ′〉, denoted LPA. PA− is the theory of the positive part of discretely ordered rings in this language, consisting of e.g. the commutative, associate and distributive laws, the recursion equations for addition and multiplication, and ordering axioms. (See [2] page 16 for the exact definition of PA−.) The arithmetic hierarchy is a family of formula classes within PA and is defined as follows:
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تاریخ انتشار 2007