Axioms Course
This course introduces formal systems through first-order logic, proofs, models, and algebraic theories, with practical applications in proof assistants and verification.

flexible workload from 4 to 360h
valid certificate in your country
What will I learn?
The Axioms Course provides a short, practical way into formal systems, starting from first-order languages and proof rules up to models, soundness, and completeness. You will look into a specific algebraic theory, check the right-identity and inverse laws, and understand how countermodels function. Link these concepts to proof assistants, model finders, and verification processes that you can use straight away in higher studies and research.
Elevify advantages
Develop skills
- Build algebraic models: quickly set up and test small group-like systems.
- Verify axioms in practice: check associativity, identities, and inverses quickly.
- Use models to refute claims: find countermodels and prove non-provability.
- Translate axioms into proofs: create clear first-order derivations step by step.
- Encode algebraic theories in proof assistants: basics of Coq, Lean, and Isabelle.
Suggested summary
Before starting, you can change the chapters and workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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