I've seen from various sources that NBG can be written with finitely many axioms. But I've been struggling for a while to find a list of these axioms, every list I can find uses an axiom of schema in one form or another. Example nlab uses a schema for Class comprehension. My question is what are the axioms of NBG without using a schema.
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$\begingroup$ Refrain from adding links, this forces viewers to click in the link to understand your question. $\endgroup$– Jonathan XuCommented Aug 12 at 2:49
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$\begingroup$ The comprehension schema can be replaced with a finite number of instances, known as the Gödel operations. Jech covers this, albeit in the guise of axiomatizing $\Delta_0$-comprehension for transitive models of ZFC, but a slight modification gives a proof that NBG is finitely axiomatizable. $\endgroup$– spaceisdarkgreenCommented Aug 12 at 2:53
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$\begingroup$ Smullyan, Set Theory and the Continuum Problem uses NBG and describes the axioms (and also provides the proof alluded to by spaceisdark green above). $\endgroup$– PorkyCommented Aug 12 at 3:05
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3$\begingroup$ en.wikipedia.org/wiki/… $\endgroup$– LucenapositionCommented Aug 12 at 6:38
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$\begingroup$ It's also covered in Mendelson's Introduction to Set Theory. $\endgroup$– Rob ArthanCommented Aug 12 at 21:26
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