Axioms Course
This course provides a practical introduction to formal systems and algebraic theories, focusing on building models, verifying axioms, using countermodels, developing proofs, and applying concepts in proof assistants like Coq, Lean, and Isabelle.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
The Axioms Course offers a compact, practical introduction to formal systems, covering first-order languages, proof rules, models, soundness, and completeness. It delves into a targeted algebraic theory, examining right-identity and inverse laws, and demonstrates the use of countermodels. These concepts link to proof assistants, model finders, and verification processes applicable right away in higher studies and research.
Elevify advantages
Develop skills
- Build algebraic models: swiftly set up and examine small group-like structures.
- Verify axioms practically: rapidly assess associativity, identities, and inverses.
- Employ models to counter claims: identify countermodels and establish non-provability.
- Convert axioms to proofs: develop precise first-order derivations progressively.
- Implement algebraic theories in proof assistants: fundamentals 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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