In this program
- Propositional and predicate logic
- Proof systems and completeness
- Axiomatic set theory
Axiomatic set theory
Mathematical logic & set theory · Theoretical / proof-based
Zermelo–Fraenkel axioms (ZFC)
Objectives
- Zermelo–Fraenkel axioms (ZFC)
- The cumulative hierarchy
- Ordinals and cardinals; cardinality and Cantor's theorem
- Axiom of choice
- Well-ordering (equivalents overview)
- Construction of number systems from set theory
- Russell's paradox
- Limitations of naive set theory
Study materials
- Study guideComing soon
- Exam StrategyComing soon
- Common MistakesComing soon
- WorksheetsComing soon
- Word problemsComing soon
- Mixed PracticeComing soon
- Multi-Unit ProblemsComing soon
- ReviewComing soon
- Practice testComing soon
- Answer keyComing soon
Interactive practice
Quizzes, typed answers, and flashcards for this unit — coming soon.
- Coming soon
Quiz
Multiple-choice questions with instant feedback
- Coming soon
Typed practice
Type answers and check them
- Coming soon
Flashcards
Vocabulary and key facts
- Coming soon
Mixed quiz
Harder mixed review for this standard