All Questions
Tagged with foundations new-foundations
7 questions
11
votes
3
answers
2k
views
What governs our "perception?" about the platonic realm of sets?
Here, I want to delve into what do we exactly feel about what constitutes a platonic existence of a set? Or what makes us think or actually a kind of feel or sense the existence of a set in the ...
- 11.3k
17
votes
0
answers
509
views
The free complete lattice on three generators, beyond ZF
This was originally asked at MSE; although it is still under bounty it seems unlikely to be answered there.
$\mathsf{ZF}$ proves that there is no free complete lattice on three generators since any ...
- 21.1k
6
votes
1
answer
375
views
What drawbacks are there to using NF(U) for category theory?
In category theory, you often run into what is known as "size" issues. That is, you run into the issue that the categories you try to define are too "big" to be sets, and so you need to use classes or ...
- 6,353
4
votes
2
answers
548
views
Anti-foundational set theory with a universal set
There are alternative set theories that allow for a universal set, e.g. NF(U), positive set theory and and topological set theory. There are also alternative set theories like ZFA that allow for the ...
- 1,228
1
vote
0
answers
257
views
Is there a non-trivial consistency preserving transformation?
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 ...
user36136
15
votes
4
answers
2k
views
Where is the end of universe?
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 ...
user36136
17
votes
10
answers
7k
views
Set theory and alternative foundations
Every foundational system for mathematics I have ever read about has been a set theory, from ETCS to ZFC to NF. Are there any proposals for a foundational system which is not, in any sense, a set ...
- 555