Formula, Operator, Logical Class and Logical Equivalence; Denumerable-Model Theorem

  • Roland Fraïssé
Part of the Synthese Library book series (SYLI, volume 54)


Given a finite sequence of positive integers i 1,…,ir, we define the indefinite quantifier, denoted by \(\mathop \forall \limits_{{i_1}, \ldots ,{i_r}} \), to be the set of quantifiers \(\mathop {\forall _m }\limits_{{i_1}, \ldots ,ir} \) in which the indices i 1,…,i r are fixed, while the predicarity m and arity n range over all values compatible with these indices. That is, nm and each of the integers n + 1,…, m is one of the indices i 1,…,ir (recall that m need not be greater than the indices). The indefinite quantifier \(\mathop \exists \limits_{{i_1}, \ldots ,{i_r}} \) is similarly defined.


Logical Operator Logical Class Logical Formula Free Part Separable Index 
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© Springer Science+Business Media Dordrecht 1973

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  • Roland Fraïssé

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