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searching for Peano axioms 5 found (85 total)

Typographical Number Theory (798 words) [view diff] exact match in snippet view article find links to article

explain Gödel's incompleteness theorems. Like any system implementing the Peano axioms, TNT is capable of referring to itself (it is self-referential). TNT

ST type theory (944 words) [view diff] exact match in snippet view article find links to article

number of types poses no difficulty. These facts, reminiscent of the Peano axioms, make it convenient and conventional to assign a natural number to each

Zermelo's categoricity theorem (385 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathrm {ZFC} ^{2}} .p. 9 Dedekind proved that the second-order Peano axioms hold in a model if and only if the model is isomorphic to the true natural

Counter machine (4,601 words) [view diff] exact match in snippet view article find links to article

because it uses the 'successor operation' of, and closely resembles, the Peano axioms. Used as a base for the successor RAM model. Uses instruction set (2)

Brouwer–Hilbert controversy (4,441 words) [view diff] case mismatch in snippet view article find links to article

Turing's machines as a formal logical system to replace his system (Peano Axioms + recursion) appear in Martin Davis, The Undecidable): Hilbert (1904)