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	abelian group is divisible if and only if it is an injective object AbelianGroupsOfOrder120 abelian groups of order 120 Abelianization abelianization AbelianNumberField abelian number field AbelianVariety abelian variety AbelPrize Abel Prize AbelsLemma AbelsLimitTheorem AbelsMultiplicationRuleForSeries AbelSummability Abel summability Abel’s lemma Abel’s limit theorem Abel’s multiplication rule for series ABIsConjugateToBA AB is conjugate to BA AbnormalSubgroup abnormal subgroup AbsoluteConvergenceImpliesConvergenceForAnInfiniteProduct absolute convergence implies convergence for an infinite product