Dependency tree

An arrow runs from a page to a page that rests on it: page B points at page A when some result on A depends, through the item graph, on a result whose home is B. Only pages in Foundations are shown; anything this group rests on from elsewhere in the library is listed below.

Pages, prerequisites first

• The ZFC Axioms and the Basic Set ConstructionsExamples & counterexamples →
• Relations, Functions, and QuotientsExamples & counterexamples →
• Construction of the Natural Numbers
• Order, Zorn's Lemma, and the Axiom of ChoiceExamples & counterexamples →
• Filters and UltrafiltersExamples & counterexamples →
• Ordinals, Cardinals, and Transfinite Recursion
• Ordinal Arithmetic and the First Uncountable OrdinalExamples & counterexamples →
• Cardinal Arithmetic, Cofinality and the AlephsExamples & counterexamples →

Rests on other groups

• Cardinal Arithmetic, Cofinality and the Alephs rests on Binary Operations, Monoids, Groups and Subgroups, Compactness in Metric Spaces, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Linear Independence, Bases and Dimension, Roots, Rational Powers, and Classical Inequalities, Sequences and Limits, Set Theory Beyond Choice: Recorded, Not Proved Here, Suprema and Infima, Vector Spaces, Linear Subspaces, Span and Direct Sums
• Cardinal Arithmetic, Cofinality and the Alephs — Examples rests on Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Monotone Sequences, Bolzano-Weierstrass, and Cauchy Completeness, Roots, Rational Powers, and Classical Inequalities, Sequences and Limits, Series: Convergence and the Nonnegative Tests, Set Theory Beyond Choice: Recorded, Not Proved Here, Suprema and Infima, The Cantor Set, Baire Category, and Measure Zero in ℝ
• Filters and Ultrafilters rests on Set Theory Beyond Choice: Recorded, Not Proved Here
• Order, Zorn's Lemma, and the Axiom of Choice rests on Set Theory Beyond Choice: Recorded, Not Proved Here
• Order, Zorn's Lemma, and the Axiom of Choice: Examples and Counterexamples rests on Set Theory Beyond Choice: Recorded, Not Proved Here
• Ordinal Arithmetic and the First Uncountable Ordinal rests on Binary Operations, Monoids, Groups and Subgroups, Compactness in Metric Spaces, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Linear Independence, Bases and Dimension, Sequences and Limits, Set Theory Beyond Choice: Recorded, Not Proved Here, Suprema and Infima, Vector Spaces, Linear Subspaces, Span and Direct Sums
• Ordinal Arithmetic and the First Uncountable Ordinal — Examples rests on Binary Operations, Monoids, Groups and Subgroups, Compactness in Metric Spaces, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Linear Independence, Bases and Dimension, Sequences and Limits, Set Theory Beyond Choice: Recorded, Not Proved Here, Vector Spaces, Linear Subspaces, Span and Direct Sums
• Ordinals, Cardinals, and Transfinite Recursion rests on Binary Operations, Monoids, Groups and Subgroups, Compactness in Metric Spaces, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Linear Independence, Bases and Dimension, Sequences and Limits, Set Theory Beyond Choice: Recorded, Not Proved Here, Vector Spaces, Linear Subspaces, Span and Direct Sums
• Relations, Functions, and Quotients: Examples and Counterexamples rests on Set Theory Beyond Choice: Recorded, Not Proved Here