zfc การใช้

• The Boolean-valued models of ZFC are a related subject.
• All formulations of ZFC imply that at least one set exists.
• I said ZFC doesn't have such a proof either.
• ZFC, however, is still formalized in classical logic.
• ZFC implies that the model of ZFC whenever ? is strongly inaccessible.
• ZFC implies that the model of ZFC whenever ? is strongly inaccessible.
• Her example fuelled the search for " small " ZFC Dowker spaces.
• In ZFC there cannot be a set of all ordinals.
• It is a general set definition in comparison to ZFC!
• Neither of these results are provable in ZFC alone.
• Peano arithmetic is provably consistent from ZFC, but not from within itself.
• There are many equivalent formulations of the ZFC axioms.
• For a complete argument that V satisfies ZFC see.
• In other words, ZFC cannot be finitely axiomatized.
• Theories obtained this way include ZFC and Peano arithmetic.
• ZFC and ZFC + CH are either both internally consistent or both not.
• ZFC and ZFC + CH are either both internally consistent or both not.
• One such system is ZFC with the axiom of infinity replaced by its negation.
• The metamathematics of ZFC has been extensively studied.
• On the other hand, among axiomatic set theories, ZFC is comparatively weak.