The quantifier complexity of polynomial-size iterated definitions in first-order logic
نویسندگان
چکیده
منابع مشابه
The quantifier complexity of polynomial-size iterated definitions in first-order logic
We refine the constructions of Ferrante-Rackoff and Solovay on iterated definitions in first-order logic and their expressibility in with polynomial size formulas. These constructions introduce additional quantifiers; however, we show that these extra quantifiers range over only finite sets. We prove optimal upper and lower bounds on the quantifier complexity of polynomial size formulas obtaine...
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We say that a first order sentence A defines a digraph G if A is true on G but false on any digraph non-isomorphic to G. Let Da(G) (resp. La(G)) denote the minimum quantifier rank (resp. length) of a such sentence in which negations occur only in front of atomic subformulas and any sequence of nested quantifiers has at most a quantifier alternations. We define the succinctness function qa(n) to...
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ژورنال
عنوان ژورنال: Mathematical Logic Quarterly
سال: 2010
ISSN: 0942-5616
DOI: 10.1002/malq.200910111