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What does that mean though? Does it only mean that ZFC is consistent when subsumed within a strongly-typed higher order theory, or does it mean that ZFC by its
by bjornsing 7y ago
What does that mean though?
Does it only mean that ZFC is consistent when subsumed within a strongly-typed higher order theory, or does it mean that ZFC by itself is consistent?
- petters 7y agoThat ZFC by itself is consistent, i.e. you can't find a contradiction.
- ProfHewitt 7y agoThe strongly-typed higher-order theory Ordinals is consistent because it has a unique up to isomorphism model by a unique isomorphism. Consequently, ZFC is consistent because it is a special case of the theory Ordinals.