Axioms Course
This course introduces formal systems through first-order logic, algebraic theories, proofs, models, and their applications in 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 path into formal systems, from first-order languages and proof rules to models, soundness, and completeness. Explore a focused algebraic theory, test right-identity and inverse laws, and see how countermodels work. Connect these ideas to proof assistants, model finders, and verification workflows you can apply immediately 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 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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