<LATEX language="en">
<![CDATA[
Axiomatic Set Theory
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Axiomatische Mengenlehre
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Preface\label{ch:preface}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Vorwort\label{ch:preface}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Introduction\label{ch:introduction}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Einleitung\label{ch:introduction}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Basics
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Anfangsgründe
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Classes and Sets
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Klassen und Mengen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Membership Operator
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Elementbeziehung
]]>
</LATEX>
#1 \in #2
<LATEX language="en">
<![CDATA[
Non Membership Operator
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Negation der Elementbeziehung
]]>
</LATEX>
#1 \notin #2
<LATEX language="en">
<![CDATA[
Extensionality\index{axiom!of extensionality}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Extensionalität\index{Extensionalitätsaxiom}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Set\index{set!definition}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Menge\index{Menge!Definition}
]]>
</LATEX>
\mathfrak{M}(#1)
<LATEX language="en">
<![CDATA[
Comprehension
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Komprehension
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Class definition
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Klassenschreibweise
]]>
</LATEX>
M(x) n alpha(x)
Im Folgenden wird auf diese Schreibweise zurückgegriffen.
]]>
<LATEX language="en">
<![CDATA[
Special Classes
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Spezielle Klassen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Russell Class\index{Russell!class of}\index{class!Russell}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Russell-Klasse\index{Russell!-sche Klasse}\index{Klasse!Russellsche}
]]>
</LATEX>
\mathfrak{Ru}
<LATEX language="en">
<![CDATA[
Universal Class\index{class!universal}\index{universal class}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Allklasse\index{Klasse!All-}\index{Allklasse}
]]>
</LATEX>
\mathfrak{V}
<LATEX language="en">
<![CDATA[
Empty Class\index{empty class}\index{empty set}\index{class!empty}\index{set!empty}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Leere Klasse\index{leere Klasse}\index{leere Menge}\index{Klasse!leere}\index{Menge!leere}
]]>
</LATEX>
\emptyset
<LATEX language="en">
<![CDATA[
Boolean Algebra of Classes\index{Boolean algebra!of classes}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Boolesche Algebra der Klassen\index{Boolesche Algebra!der Klassen}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Boolean Class Operators
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Boolesche Klassenoperatoren
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Union Operator\index{union}\index{class!union}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Vereinigung\index{Vereinigung}\index{Klasse!Vereinigung}
]]>
</LATEX>
(#1 \cup #2)
<LATEX language="en">
<![CDATA[
Intersection Operator\index{intersection}\index{class!intersection}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Durchschnitt\index{Durchschnitt}\index{Klasse!Durchschnitt}
]]>
</LATEX>
(#1 \cap #2)
<LATEX language="en">
<![CDATA[
Complement Operator\index{complement}\index{class!complement}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Komplement\index{Komplement}\index{Klasse!Komplement}
]]>
</LATEX>
\overline{#1}
<LATEX language="en">
<![CDATA[
Boolean Algebra\index{Boolean algebra}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Boolsche Algebra\index{Boolesche Algebra}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Order\index{order}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Ordnung\index{Ordnung}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Subclass Predicate\index{subclass}\index{inclusion}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Teilklasse\index{Teilklasse}
]]>
</LATEX>
#1 \ \subseteq \ #2
<LATEX language="en">
<![CDATA[
Singletons and Class Pairs
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Einerklassen und Klassenpaare
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Singleton\index{singleton}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Einerklasse\index{Einerklasse}\index{Klasse!Einer-}
]]>
</LATEX>
\{ #1 \}
<LATEX language="en">
<![CDATA[
Pair\index{pair}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Paar\index{Paar}\index{Klasse!Paar-}
]]>
</LATEX>
\{ #1, #2 \}
<LATEX language="en">
<![CDATA[
Infinite Boolean Operators
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Unendliche boolsche Operatoren
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Set Product\index{set product}\index{product!of sets}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Mengenprodukt\index{Mengenprodukt}\index{Produkt!von Mengen}
]]>
</LATEX>
\bigcap \ #1
<LATEX language="en">
<![CDATA[
Set Sum\index{set sum}\index{sum!of sets}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Mengensumme\index{Mengensumme}\index{Summe!von Mengen}
]]>
</LATEX>
\bigcup \ #1
<LATEX language="en">
<![CDATA[
Power Class Building
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Potenzklassenbildung
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Power Class\index{class!power}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Potenzklasse\index{Klasse!Potenz-}
]]>
</LATEX>
\mathfrak{P}(#1)
<LATEX language="en">
<![CDATA[
Sets, Relations and Functions
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Mengen, Relationen und Funktionen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Sets
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Mengen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Empty Set Axiom\index{axiom!empty set}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Axiom der leeren Menge\index{Axiom!der leeren Menge}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Pairing Set Axiom\index{axiom!pairing set}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Axiom der Paarmenge\index{Axiom!Paarmengen-}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Axiom of the Sum Set\index{axiom!of the sum set}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Summenmengenaxiom\index{Axiom!Summenmengen-}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Power Set Axiom\index{axiom!power set}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Axiom der Potenzmenge\index{Axiom!Potenzmengen-}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Subset Axiom\index{axiom!subset}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Teilmengenaxiom\index{Axiom!Teilmengen-}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Ordered Pair
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Geordnetes Klassenpaar
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Ordered Pair\index{pair!ordered}\index{ordered pair}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Geordnetes Paar\index{geordnetes Paar}\index{Paar!geordnetes}
]]>
</LATEX>
\langle #1, #2 \rangle
<LATEX language="en">
<![CDATA[
Ordered Pair Property\index{ordered pair!property}\index{pair!ordered}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Eigenschaft geordnetes Paar\index{Paar!geordnetes}
]]>
</LATEX>
\mbox{isOrderedPair}(#1)
<LATEX language="en">
<![CDATA[
Cartesian Product
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Kartesisches Produkt
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Cartesian Product\index{product!Cartesian}\index{Cartesian product}\index{direct product}\index{product!direct}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Kartesisches Produkt\index{Produkt!kartesisches}\index{Produkt!Kreuz-}\index{Kartesisches Produkt}\index{Kreuzprodukt}
]]>
</LATEX>
( #1 \times #2)
<LATEX language="en">
<![CDATA[
Relations
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Relationen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Relation\index{relation}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Relation\index{relation}
]]>
</LATEX>
\mathfrak{Rel}(#1)
<LATEX language="en">
<![CDATA[
Domain\index{domain}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Definitionsbereich\index{Definitionsbereich}
]]>
</LATEX>
\mathfrak{Dom}(#1)
<LATEX language="en">
<![CDATA[
Range\index{range}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Wertebereich\index{Wertebereich}
]]>
</LATEX>
\mathfrak{Rng}(#1)
<LATEX language="en">
<![CDATA[
Relation Algebra
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Relationenalgebra
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Equivalence Relations
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Äquivalenzrelationen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Maps and Functions
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Abbildungen und Funktionen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Function\index{function}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Funktion\index{Funktion}
]]>
</LATEX>
\mathfrak{Funct}(#1)
<LATEX language="en">
<![CDATA[
Fraenkel's Replacement Axiom\index{axiom!of replacement}\index{Fraenkel's replacement axiom}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Fraenkelsches Ersetzungsaxiom\index{Axiom!Fraenkelsches Ersetzungs-}\index{Substitutionsaxiom}\index{Fraenkel}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Natural Numbers
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Natürliche Zahlen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Foundation and Infinity
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Fundierung und Unendlichkeit
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Axiom of Foundation\index{axiom!of foundation}\index{axiom!of regularity}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Fundierungsaxiom\index{Axiom!Fundierungs-}\index{Axiom!Regularitäts-}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Successor\index{successor}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Nachfolger\index{Nachfolger}
]]>
</LATEX>
#1'
<LATEX language="en">
<![CDATA[
Axiom of Infinity\index{infinity!axiom of}\index{axiom!of infinity}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Unendlichkeits\index{Unendlichkeit!-saxiom}\index{Axiom!Unendlichkeits-}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Definition and Basic Properties
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Definition und Grundeigenschaften
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Induction
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Induktion
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Sequences and Normal Functions
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Folgen und normale Funktionen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Recursion
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Rekursion
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Axiom of Choice
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Auswahlaxiom
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Well-Ordering
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Wohlordnungen
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Axiom of Choice\index{axiom!of foundation}
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Auswahlaxiom\index{Axiom!Auswahl-}
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Applications of the Axiom of Choice
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Anwendungen des Auswahlaxioms
]]>
</LATEX>
<LATEX language="en">
<![CDATA[
Continuum
]]>
</LATEX>
<LATEX language="de">
<![CDATA[
Kontinuum
]]>
</LATEX>
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