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

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

Abstract

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.

Keywords

Logical Operator Logical Class Logical Formula Free Part Separable Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1973

Authors and Affiliations

  • Roland Fraïssé

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