Index of notation

The reference numbers indicate the chapter, section, and subsection, in that order. (R refers to the Summary of Results.)

$\square$, $\tau$, $\vee$, $\neg$, $\Rightarrow$ : I.1.1

$\tau_x(A)$, $(B\mid x)A$, $A\{x\}$, $A\{x,y\}$, $A\{B\}$, $A\{B,C\}$ : I.1.1

not $(A)$, $(A)$ or $(B)$, $(A)\Rightarrow(B)$ : I.2

“$A$ and $B$” : I.3.4

$\Longleftrightarrow$, $A\Longleftrightarrow B$ : I.3.5

$(\exists x)R$, $(\forall x)R$ : I.4.1

$(\exists_Ax)R$, $(\forall_Ax)R$ : I.4.4

$=$, $\ne$, $T=U$, $T\ne U$ : I.5.1

$\in$, $\notin$, $T\in U$, $T\notin U$ : II.1.1

$\subset$, $\supset$, $\not\subset$, $\not\supset$, $x\subset y$, $x\supset y$ : II.1.2

$\mathrm{Coll}_xR$, $\varepsilon_x(R)$ : II.1.4

$\{x,y\}$, $\{x\}$ : II.1.5

$C_XA$, $X-A$, $CA$, $\varnothing$ : II.1.7

$\supset$, $(T,U)$, $\operatorname{pr}_1z$, $\operatorname{pr}_2z$ : II.2.1

$A\times B$, $A\times B\times C$, $A\times B\times C\times D$, $(x,y,z)$ : II.2.2

$\operatorname{pr}_1\langle G\rangle$, $\operatorname{pr}_2\langle G\rangle$, $\operatorname{pr}_1G$, $\operatorname{pr}_2G$ (G a graph) : II.3.1

$G\langle X\rangle$, $G(X)$, $G(x)$ (G a graph, X a set, x an object) : II.3.1

$\Gamma\langle X\rangle$, $\Gamma(X)$, $\Gamma(x)$ ($\Gamma$ a correspondence, X a set, x an object) : II.3.1

$\overset{-1}{G}$ (G a graph), $\overset{-1}{\Gamma}$ ($\Gamma$ a correspondence) : II.3.2

$G'\circ G$, $G'G$ (G, G' graphs), $\Gamma'\circ\Gamma$, $\Gamma'\Gamma$ ($\Gamma$, $\Gamma'$ correspondences) : II.3.3

$\Delta_A$, $I_A$ (A a set) : II.3.3

$f(x)$, $f_x$ (f a function), $F(x)$, $F_x$ (F a functional graph) : II.3.4

$\operatorname{Is}(\Gamma,\Gamma'),\ \operatorname{Ord}(E),\ \lambda<\mu,\ \sum_{i\in I}\lambda_i,\ \prod_{i\in I}\lambda_i,\ \lambda+\mu,\ \mu\lambda,\ \lambda^*(\lambda,\mu,\lambda,\text{order-types})$ : III.2, Exercise 13

$\xi^\eta$ ($\xi,\eta$ ordinals) : III.2, Exercise 18

$\operatorname{Eq}(X,Y),\ \operatorname{Card}(X)$ : III.3.1

$0,1,2$ : III.3.1

$\mathfrak{c}\leq\mathfrak{d}$ ($\mathfrak{c},\mathfrak{d}$ cardinals) : III.3.2

$\sup_{i\in I}a_i,\ ((a_i)_{i\in I}$ a family of cardinals) : III.3.2

$\sum_{i\in I}a_i,\ \prod_{i\in I}a_i,\ \prod_{i\in I}((a_i)_{i\in I}$ a family of cardinals) : III.3.3

$a+b,\ ab$ ($a,b$ cardinals) : III.3.3

$a^b$ ($a,b$ cardinals) : III.3.5

$3,4$ : III.4.1

$a-b$ ($a,b$ integers, $b<a$) : III.5.2

$(t_i)_{i\in I},\ (t_i)_{a\leq i\leq b}$ : III.5.4

$\prod_{i\in I}X_i,\ \prod_{i=a}^{b}X_i$ : III.5.4

$\varphi_A$ ($A$ a subset of a set $E$) : III.5.5

$\frac{a}{b},\ a/b$ ($a,b$ integers such that $b$ divides $a$) : III.5.6

$5,6,7,8,9$ : III.5.7

$n!$ ($n$ an integer) : III.5.8

$\binom{n}{p}$ ($n,p$ integers) : III.5.8

$\mathbf{N},\ \aleph_0$ : III.6.1

$(x_n)_{n\in\mathbf{N}},\ (x_n)_{k\leq n},\ (x_n)_{n\geq k},\ (x_n)$ : III.6.1

$\prod_{n\in\mathbf{N}}X_n,\ \prod_{n=k}^{\infty}X_n$ : III.6.1

$f^n$ ($f$ a mapping) : III.6.2

$\omega_\alpha,\ \aleph_\alpha$ ($\alpha$ an ordinal) : III.6, Exercise 10

$\lim_{\leftarrow}E_\alpha$ ($E_\alpha$ sets) : III.7.1

$\lim_{\leftarrow}u_\alpha$ ($u_\alpha$ mappings) : III.7.2

$\lim_{\alpha,\lambda\leftarrow}E^\lambda_\alpha,\ \lim_{\alpha\leftarrow}E^\lambda_\alpha,\ \lim_{\alpha,\lambda\leftarrow}u^\lambda_\alpha,\ \lim_{\alpha\leftarrow}u^\lambda_\alpha$ : III.7.3

$\lim_{\alpha\leftarrow}E_\alpha$ ($E_\alpha$ sets) : III.7.5

$\lim_{\alpha\rightarrow}u_\alpha$ ($u_\alpha$ mappings) : III.7.6

$\displaystyle \lim_{\overrightarrow{\alpha,\lambda}} E_\alpha^\lambda,\ \lim_{\overrightarrow{\alpha}} E_\alpha^\lambda,\ \lim_{\overrightarrow{\alpha,\lambda}} u_\alpha^\lambda,\ \lim_{\overrightarrow{\alpha}} u_\alpha^\lambda :$ III.7.7

$S(E_1,\ldots,E_n)$ (S an echelon construction scheme, $E_1,\ldots,E_n$ sets) : IV.1.1

$\langle f_1,\ldots,f_n\rangle^s$ (S an echelon construction scheme, $f_1,\ldots,f_n$ mappings) : IV.1.1

$R\{x,y,z\}$ : R.1.2

$=,\ne$ : R.1.6

$\in,\notin$ : R.1.7

$\complement A,\ E-A$ : R.1.7

$\varnothing$ : R.1.8

$\{a\}$ : R.1.9

$\mathfrak{P}(E)$ : R.1.10

$\subset,\supset,\subsetneqq,\supsetneqq$ : R.1.12

$\cup,\cap$ : R.1.13

$\{x,y,z\}$ : R.1.13

$X_A$ (X a subset) : R.1.16

$\mathscr{E}_A$ ($\mathscr{E}$ a set of subsets) : R.1.16

$f(x),\ f_x,\ x\to f(x)$ ($f$ a mapping, $x$ an element) : R.2.2

$f(X)$ (X a subset) : R.2.4

$f^{-1}$ ($f$ a mapping) : R.2.6

$g\circ f,\ h\circ g\circ f$ ($f,g,h$ mappings) : R.2.11

$f_A$ ($f$ a mapping) : R.2.13

$(x_i)_{i\in I},\ (x_i)$ : R.2.14

$(x,y)$ : R.3.1

$E\times F$ (E, F sets) : R.3.1

$\operatorname{pr}_1,\operatorname{pr}_2$ : R.3.1

$\Delta$ : R.3.4

$Z^{-1}$ (Z a subset of a product) : R.3.4

$K(X)$ (K a subset of $E\times F$, X a subset of E) : R.3.6

$K(x)$ (K a subset of $E\times F$, x an element of E) : R.3.9

$B\circ A,\ BA,\ C\circ B\circ A,\ CBA$ (A a subset of $E\times F$, B a subset of $F\times G$, C a subset of $G\times H$) : R.3.10

$(x,y,z)$ : R.3.12

$E\times F\times G$ : R.3.12

$\operatorname{pr}_{1,2}$ : R.3.12