Mathlib Map

Theorems · Definition · logic and foundations

Ordinal.IsInitial

Ordinal.{u_1} → Prop

An ordinal is initial when it is the first ordinal with a given cardinality. This is written as o.card.ord = o, i.e. o is the smallest ordinal with cardinality o.card.

Defined in
Mathlib.SetTheory.Cardinal.Aleph
Cited by
28 results in Mathlib
Foundations
Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cardinal.preAleph · cited by 44Cardinal.preAlephOrdinal.preOmega · cited by 31Ordinal.preOmegaOrdinal.IsInitial.ord_card · cited by 4IsInitial.ord_cardOrdinal.isInitial_natCast · cited by 4Ordinal.isInitial_natCastOrdinal.isInitial_omega · cited by 4Ordinal.isInitial_omegaOrdinal.isInitial_preOmega · cited by 3Ordinal.isInitial_preOmegaOrdinal.not_bddAbove_isInitial · cited by 3Ordinal.not_bddAbove_isIn…Ordinal.isInitial_ord · cited by 3Ordinal.isInitial_ordOrdinal.IsInitial.isPrincipal_add · cited by 2IsInitial.isPrincipal_addOrdinal.IsInitial.isPrincipal_mul · cited by 2IsInitial.isPrincipal_mulOrdinal.IsInitial.isPrincipal_opow · cited by 2IsInitial.isPrincipal_opowOrdinal.IsInitial.card_lt_card · cited by 2IsInitial.card_lt_cardOrdinal.isInitialIso · cited by 2Ordinal.isInitialIsoOrdinal.IsInitial.le_ord_iff_card_le · cited by 1IsInitial.le_ord_iff_card…Ordinal.IsInitial.mem_range_preOmega · cited by 1IsInitial.mem_range_preOm…Ordinal · cited by 1688OrdinalCardinal.ord · cited by 266Cardinal.ordOrdinal.card · cited by 122Ordinal.cardOrdinal.IsInitialCITED BYCITES

Cites3

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Cited by31

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