Changes

We may understand the enlarged proposition <math>\operatorname{E}f</math> as telling us all the different ways to reach a model of <math>f\!</math> from any point of the universe <math>U.\!</math>

We may understand the enlarged proposition <math>\operatorname{E}f</math> as telling us all the different ways to reach a model of <math>f\!</math> from any point of the universe <math>U.\!</math>

To broaden our experience with simple examples, let us now contemplate the sixteen functions of concrete type <math>X \times Y \to \mathbb{B}</math> and abstract type <math>\mathbb{B} \times \mathbb{B} \to \mathbb{B}.</math>  For future reference, I will set here a few Tables that detail the actions of <math>\operatorname{E}</math> and <math>\operatorname{D}</math> on each of these functions, allowing us to view the results in several different ways.

To broaden our experience with simple examples, let us now contemplate the sixteen functions of concrete type <math>X \times Y \to \mathbb{B}</math> and abstract type <math>\mathbb{B} \times \mathbb{B} \to \mathbb{B}.</math>  For future reference, I will set here a few Tables that detail the actions of <math>\operatorname{E}</math> and <math>\operatorname{D}</math> on each of these functions, allowing us to view the results in several different ways.