A.1.5 The finite types

We introduce primitive constants $\\star$ , $\\mathbf{0}$ , $\\mathbf{1}$ , satisfying the following rules:

•
$\\mathbf{0}:\\mathcal{U}_{0}$ , $\\mathbf{1}:\\mathcal{U}_{0}$
•
$\\star:\\mathbf{1}$

Given $C:\\mathbf{0}\\rightarrow\\mathcal{U}_{n}$ we can introduce a defined constant $f:\\mathchoice{{\\textstyle\\prod_{(x:\\mathbf{0})}}}{\\prod_{(x:\\mathbf{0})}}{%\\prod_{(x:\\mathbf{0})}}{\\prod_{(x:\\mathbf{0})}}C(x)$ , with no defining equations.

Given $C:\\mathbf{1}\\rightarrow\\mathcal{U}_{n}$ and $d:C(\\star)$ we can introduce a defined constant $f:\\mathchoice{{\\textstyle\\prod_{(x:\\mathbf{1})}}}{\\prod_{(x:\\mathbf{1})}}{%\\prod_{(x:\\mathbf{1})}}{\\prod_{(x:\\mathbf{1})}}C(x)$ , with defining equation $f(\\star):\\!\\!\\equiv d$ .

单词	A15TheFiniteTypes
释义	A.1.5 The finite types We introduce primitive constants $\\star$ , $\\mathbf{0}$ , $\\mathbf{1}$ , satisfying the following rules: • $\\mathbf{0}:\\mathcal{U}_{0}$ , $\\mathbf{1}:\\mathcal{U}_{0}$ • $\\star:\\mathbf{1}$ Given $C:\\mathbf{0}\\rightarrow\\mathcal{U}_{n}$ we can introduce a defined constant $f:\\mathchoice{{\\textstyle\\prod_{(x:\\mathbf{0})}}}{\\prod_{(x:\\mathbf{0})}}{%\\prod_{(x:\\mathbf{0})}}{\\prod_{(x:\\mathbf{0})}}C(x)$ , with no defining equations. Given $C:\\mathbf{1}\\rightarrow\\mathcal{U}_{n}$ and $d:C(\\star)$ we can introduce a defined constant $f:\\mathchoice{{\\textstyle\\prod_{(x:\\mathbf{1})}}}{\\prod_{(x:\\mathbf{1})}}{%\\prod_{(x:\\mathbf{1})}}{\\prod_{(x:\\mathbf{1})}}C(x)$ , with defining equation $f(\\star):\\!\\!\\equiv d$ .
随便看	example of cylindric algebra ExampleOfDefinableType example of definable type ExampleOfDeRhamCohomology example of de Rham cohomology ExampleOfDerivativeAsParameter example of derivative as parameter ExampleOfDifferentiableFunctionWhichIsNotContinuouslyDifferentiable example of differentiable function which is not continuously differentiable ExampleOfDifferentiationUnderIntegralSign example of differentiation under integral sign ExampleOfDiracSequence example of Dirac sequence ExampleOfDividedDifferenceInterpolaton example of divided difference interpolaton ExampleOfDivisibleGroup example of divisible group ExampleOfEliminatingHigherorderDerivatives example of eliminating higher-order derivatives ExampleOfFalseImpliesTrue example of false implies true ExampleOfFermatsLastTheorem example of Fermat’s last theorem ExampleOfFibreProduct example of fibre product