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.
|Date of creation||2013-03-22 12:59:16|
|Last modified on||2013-03-22 12:59:16|
|Last modified by||Henry (455)|