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Härtig's quantifier is a quantifier which takes two variables and two formulas, written
. It asserts that
. That is, the cardinality of the values of which make is the same as the cardinality of the values which make true. Viewed as a generalized quantifier, is a
quantifier.
Closely related is the Rescher quantifier, which also takes two variables and two formulas, is written
, and asserts that
. The Rescher quantifier is sometimes defined instead to be a similar but different quantifier,
. The first definition is a
quantifier while the second is a
quantifier.
Another similar quantifier is Chang's quantifier , a
quantifier defined by
. That is,
is true if the number of satisfying has the same cardinality as the universe; for finite models this is the same as , but for infinite ones it is not.
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