Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
axiomatic system
mathematical logic concept |
| gptkbp:alternativeName |
gptkb:Peano_postulates
|
| gptkbp:axiom1 |
0 is a natural number
|
| gptkbp:axiom2 |
every natural number has a unique successor
|
| gptkbp:axiom3 |
0 is not the successor of any natural number
|
| gptkbp:axiom4 |
distinct natural numbers have distinct successors
|
| gptkbp:axiom5 |
if a set contains 0 and is closed under successor, it contains all natural numbers (induction axiom)
|
| gptkbp:category |
mathematical axioms
|
| gptkbp:consistsOf |
five axioms
|
| gptkbp:field |
gptkb:logic
gptkb:mathematics number theory |
| gptkbp:hasModel |
standard model of arithmetic
|
| gptkbp:hasNonStandardModel |
nonstandard models of arithmetic
|
| https://www.w3.org/2000/01/rdf-schema#label |
Peano axioms
|
| gptkbp:influenced |
gptkb:logic
gptkb:set_theory foundations of mathematics |
| gptkbp:introduced |
gptkb:Giuseppe_Peano
|
| gptkbp:introducedIn |
1889
|
| gptkbp:language |
first-order language with equality, 0, and successor function
|
| gptkbp:purpose |
formalize the natural numbers
|
| gptkbp:relatedTo |
gptkb:first-order_logic
gptkb:second-order_logic natural numbers |
| gptkbp:usedFor |
foundation of arithmetic
|
| gptkbp:bfsParent |
gptkb:Giuseppe_Peano
gptkb:Axiom_of_Infinity gptkb:Foundations_of_mathematics gptkb:Zermelo-Fraenkel_set_theory |
| gptkbp:bfsLayer |
5
|