Axioms Course
This course offers a practical introduction to formal systems and algebraic theories, emphasizing hands-on skills in modeling, verification, and proof construction using proof assistants.

from 4 to 360h 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, proof rules, models, soundness, and completeness. It delves into a focused algebraic theory, testing right-identity and inverse laws, and demonstrates how countermodels function. Participants connect these concepts to proof assistants, model finders, and verification workflows applicable in advanced studies 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 fast.
- 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: Coq, Lean, and Isabelle basics.
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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