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Peano system

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Summary

A set with zero and successor satisfying the second-order Peano axioms.

Record metadata

Carrier(s)

Data

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

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Successor structurePeano system

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Require successor injectivity, zero not to be a successor, and the adopted second-order induction axiom.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Peano systemNatural numbers N\mathbb N

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

N\mathbb N on carrier ω\omega is the standard second-order Peano system.

How to interpret this relation type

The target is a member or subtype of the broader source class.

Relation sources