Symmetric propositions and logical quantifiers

Journal of Philosophical Logic 37 (6):575 - 591 (2008)
Symmetric propositions over domain and signature are characterized following Zermelo, and a correlation of such propositions with logical type- quantifiers over is described. Boolean algebras of symmetric propositions over and Σ are shown to be isomorphic to algebras of logical type- quantifiers over . This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only those invariant under domain permutations.
Keywords generalized quantifier  logical notion  symmetric proposition
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