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Revision as of 20:20, 9 December 2008
, 20:20, 9 December 2008→Option 1 : Less General: restoring original section on option 1
Finally, it is often convenient to write the first argument as a subscript, hence <math>\Upsilon_e \langle f \rangle = \Upsilon \langle e, f \rangle.</math>
Finally, it is often convenient to write the first argument as a subscript, hence <math>\Upsilon_e \langle f \rangle = \Upsilon \langle e, f \rangle.</math>
As a special application of this operator, we next define the absolute umpire operator, also called the "umpire measure". This is a higher order proposition <math>\Upsilon_1 : (\mathbb{B}^2 \to \mathbb{B}) \to \mathbb{B}</math> which is given by the relation <math>\Upsilon_1 \langle f \rangle = \Upsilon \langle 1, f \rangle.</math>
As a special application of this operator, we next define the absolute umpire operator, also called the "umpire measure". This is a higher order proposition <math>\Upsilon_1 : (\mathbb{B}^2 \to \mathbb{B}) \to \mathbb{B}</math> which is given by the relation <math>\Upsilon_1 \langle f \rangle = \Upsilon \langle 1, f \rangle.</math> Here, the subscript "1" on the left and the argument "1" on the right both refer to the constant proposition <math>1 : \mathbb{B}^2 \to \mathbb{B}.</math>
====Option 2 : More General====
====Option 2 : More General====
