First-order theory of arithmetic axiomatised by Peano's axioms (0 is a natural, successor is injective and avoids 0, plus the induction schema). The canonical target of Gödel's first incompleteness theorem: any consistent…
Peano arithmetic (PA)
Related concepts
- Zero is a natural number
- Every natural number has a successor
- Principle of mathematical induction
- Gödel's first incompleteness theorem
- Robinson arithmetic (Q)
- Robinson arithmetic (Q)
- Presburger arithmetic
- Presburger arithmetic
- Heyting arithmetic (HA)
- Heyting arithmetic (HA)
- Wilson's theorem
- Sum-of-two-squares theorem
- Gentzen's consistency proof of PA (ε₀-induction)
- ω-consistency