Any consistent formal system F capable of expressing elementary arithmetic contains a true statement that F cannot prove.
Gödel's first incompleteness theorem
Related concepts
- Principle of mathematical induction
- Undiscovered limitative results
- Undecidability of the halting problem
- Gödel's second incompleteness theorem
- Gödel's second incompleteness theorem
- Natural numbers (ℕ)
- Undiscovered limitative results
- Peano arithmetic (PA)
- Ω (Chaitin's constant)
- Compactness theorem (FOL)
- Tarski's undefinability of truth
- ω-consistency
- Undecidability of the spectral gap in 2D quantum lattice models (Computational Physics)