Axioms Course
This course introduces formal systems, algebraic theories, proof rules, models, and their applications in verification and proof assistants.

from 4 to 360h flexible workload
certificate valid in your country
What will I learn?
The Axioms Course provides a compact, practical introduction to formal systems, covering first-order languages, proof rules, models, soundness, and completeness. You'll explore a targeted algebraic theory, test laws like right-identity and inverses, and understand how countermodels function. These concepts link to proof assistants, model finders, and verification processes that you can use right away in advanced 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 efficiently.
- Use models to refute claims: identify countermodels and demonstrate 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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