alternative set theories - Largest ordinal in NFU - Mathematics Stack Exchange
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NFU set theory sidesteps the Burali-Forti paradox by capping the ordinal hierarchy — revealing how foundational axioms quietly determine what infinity even means.
Burali-Forti ParadoxNew Foundations Set Theory (NFU)Ordinal TheoryAxiomatic Set Theory
Theory Briefing
- NFU (New Foundations with Urelements) avoids the Burali-Forti paradox by positing a largest ordinal Ω, unlike standard ZFC.
- The Burali-Forti paradox shows that assuming a set of all ordinals generates a contradiction — NFU escapes by restricting comprehension.
- Holmes' textbook frames this as a deliberate foundational trade-off: consistency is preserved by accepting a bounded ordinal universe.