ZFC vs NBG: A Comparison of Mathematical Axiom Systems

  • Thread starter Thread starter quantum123
  • Start date Start date
  • Tags Tags
    Zfc
AI Thread Summary
ZFC and NBG are both mathematical axiom systems that can prove the same theorems, making the choice between them largely subjective. The discussion emphasizes that neither system is inherently better or preferable, as their utility depends on context rather than personal preference. Some participants humorously mention personal biases, like aesthetic preferences, but these do not impact the mathematical validity of either system. Ultimately, the consensus is that the differences between ZFC and NBG are not significant enough to warrant a strong preference. The focus remains on their equivalence in mathematical proofs rather than individual opinions.
quantum123
Messages
306
Reaction score
1
Which one do you prefer? Which do you think is better?
 
Physics news on Phys.org
Neither one is better than the other, nor is one preferable to the other.
 
Er...ZFC, because it matches my curtains.
This doesn't really strike me as a "preference issue". You can prove the same things in both, so, as a fan of mathematics, I really see no reason to pick a side, since it's unlikely that I'll ever encounter a level of argument "low" enough that the difference is relevant.
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
View full post »

Similar threads

A An additional constraint to the ZFC axioms?
Replies
40
Views
4K
I Direct limit of multiverse models of ZFC
Replies
2
Views
2K
MHB ZFC and the Axiom of Power Sets ....
Replies
2
Views
2K
MHB ZFC and the Pairing Principle .... Searcoid Theorem 1.1.5 ....
Replies
1
Views
2K
A Maybe it is not necessary to define set membership?
Replies
13
Views
1K
MHB ZFC and the Axiom of Foundation
Replies
3
Views
3K
MHB Set Theory and ZFC - The Axiom of Replacement - Searcoid, Pages 6-7
Replies
14
Views
4K
Other than ZFC, what other axiomatic systems are useful?
Replies
1
Views
2K
MHB Understanding ZFC and the Axiom of Infinity: Simple Explanation and Examples
Replies
2
Views
2K
MHB Set Theory and ZFC - The Subset Principal - Searcoid, Page 7
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top