Axioms Course
This course introduces formal systems, first-order logic, algebraic theories, and their applications in proof assistants and verification.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
The Axioms Course provides a compact, hands-on introduction to formal systems, covering first-order languages and proof rules through to models, soundness, and completeness. You'll explore a focused algebraic theory, test right-identity and inverse laws, and understand how countermodels function. Link these concepts to proof assistants, model finders, and verification processes you can apply straight away in advanced study and research.
Elevify advantages
Develop skills
- Build algebraic models: quickly construct and test small group-like systems.
- Verify axioms in practice: check associativity, identities, and inverses swiftly.
- Use models to refute claims: find countermodels and prove non-provability.
- Translate axioms into proofs: craft clean 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 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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