Arithmetic definability by formulas with two quantifiers
Keyword(s):
AbstractWe give necessary conditions for a set to be definable by a formula with a universal quantifier and an existential quantifier over algebraic integer rings or algebraic number fields. From these necessary conditions we obtain some undefinability results. For example, N is not definable by such a formula over Z. This extends a previous result of R. M. Robinson.
Keyword(s):
1991 ◽
Vol 1991
(416)
◽
pp. 187-194
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Keyword(s):
2012 ◽
Vol 27
(22)
◽
pp. 1250112