Let $a$ and $b$ are two "objects". What is the meaning of $a=b$? This is one of the deepest problems of philosophy and logic because one needs a complete information about ...
In set theory "equiconsistency" (and not "consistency") of the theories is the main part of researches. So we usually try to construct a new model using a given one. In the ...
In some sense the empty set ($\emptyset$) and the global set of all sets ($G$) are the ends of the universe of mathematical objects. The world which $ZFC$ describes has an end from the bottom and is ...
So my Google-fu didn't show any references on this. I'm studying an obscure set theory (ML, a variation on NF with proper classes) and it seems to not deal well with the standard definitions of ...
By Russel's paradox, we know that the concept of the set of all sets is inconsistent. Similarly, if classes have only sets as members, the concept of the class of all classes is inconsistent because ...
Hi all! Is there anything like Gödel's constructible universe for New Foundations? More precisely, I would like a process for taking a model $M$ of NF, and using it to build a model $L \subseteq M$ ...
Hi all! I am trying to understand Specker (1953)'s proof (found here) that the axiom of choice is false in New Foundations. I am stuck on the following point. At 3.5 Specker writes: 3.5. The cardinal ...
This question might not really be considered appropriate for mathoverflow.net but I'll risk asking it and apologize in advance if I have commited a booboo. It is often said that in NF one can prove ...
I'm in search of a set theory that satisfies the following requirements. There is a universal set $V$ such that $\forall x(x \in V)$. So for example, $V \in V$. Sets whose elements are 'large' ...
New Foundations (introduced by Quine) proves that $AC$ is false. Out of curiosity, is $NF$ consistent with countable choice or dependent choice? What's the strongest consequence of choice still ...
Main Question: Does anyone know of a reference that can tell me which axioms of ZFC Quine's New Foundations prove, disprove, and leave undecided? Secondary Question: I've read that diagonal ...
[Cross-posted from here] If my understanding is correct, naive set theory needs to be restricted in order to avoid paradoxes including the Russell paradox. Typically, the restriction is expressed in ...