Axioms Course
This course introduces formal systems through first-order logic, proofs, models, and algebraic theories, with hands-on practice in verification tools like Coq and Lean.

from 4 to 360h flexible workload
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, try out right-identity and inverse laws, and learn how countermodels function. Link these concepts to proof assistants, model finders, and verification processes that you can use right away in higher studies and research.
Elevify advantages
Develop skills
- Build algebraic models: quickly set up and check small group-like systems.
- Verify axioms in practice: test associativity, identities, and inverses quickly.
- Use models to refute claims: discover countermodels and show non-provability.
- Translate axioms into proofs: create clear first-order derivations one step at a time.
- Encode algebraic theories in proof assistants: basics of Coq, Lean, and Isabelle.
Suggested summary
Before starting, you can change the chapters and the 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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