All Questions
13 questions
16
votes
2
answers
1k
views
CH in non-set theoretic foundations
I asked this question on stack exchange and got little attention, barring a nice example I intend to look into. The original post can be found here: https://math.stackexchange.com/q/4941233/1053681
I ...
- 261
43
votes
4
answers
5k
views
Lists as a foundation of mathematics
I am wondering if there is a foundation of mathematics where not sets or "set-like objects" (such as objects of a suitable topos as in ETCS) are the primitive notion, but rather lists. These ...
- 63.1k
6
votes
1
answer
205
views
How strong is separation + reflection of unbounded quantifiers?
Consider a set theory with the following axioms:
separation: $\exists y \forall x (x \in y \leftrightarrow \phi \land x \in a)$ where $y$ is not free in $\phi$
reflection: $\phi \to \exists u \phi^u$
...
- 2,203
5
votes
2
answers
629
views
Applications of ZFA-Set Theory
The set theory with atoms (ZFA), is a modified version of set theory, and is characterized by the fact that it admits objects other than sets, atoms. Atoms are objects which do not have any elements.
...
- 115
8
votes
4
answers
776
views
Self-contained formalization of random variables?
I have not been able to find any formalization of random variables that supports construction of new random variables dependent on previously constructed ones. In what I have found, a random variable $...
- 2,912
74
votes
8
answers
14k
views
Category theory and set theory: just a different language, or different foundation of mathematics?
This is a question to research mathematicians, as well as to those concerned with the history and philosophy of mathematics.
I am asking for a reference. In order to make the reference request as ...
- 6,937
1
vote
2
answers
228
views
Cardinals in $ZFC+\neg CH$
Before asking my question I like to admit that i am not an expert in the foundation of mathematics and I am interested in this issue more from a philosophical perspective. So my question may be ...
- 1,648
12
votes
1
answer
1k
views
ZF(C) and category theory
Is there an axiomatisation of some kind of category theory and a definition of sets in this framework such that the axioms of ZF resp. ZFC are theorems?
- 1,648
8
votes
1
answer
1k
views
Category theory without axiom of choice
I'm looking for references on the development of (some of) Category theory without the axiom of choice. One possible axiom system (that, to me, seems the natural setting) is ZF + there are arbitrarily ...
- 773
2
votes
3
answers
855
views
What is the largest large-cardinal hypothesis consistent with $ZFC + V=L$?
What is the largest large-cardinal hypothesis consistent with $ZFC + V=L$? The reason for the question is this: under the assumption that all of 'ordinary mathematics' (as reverse mathematics ...
- 6,132
2
votes
0
answers
264
views
About the limitation by size
This could be a big post, so I'll try to summarize my thoughts and divide them into several questions.
When working in category theory, I used to choose the following definition. A category $C$ is ...
- 1,017
5
votes
1
answer
191
views
Class theory with support for self-application of class functions?
To every natural number $n$, we can assign its Church numeral $\underline{n}.$ A formal definition would be:
$\underline{0}(f)=\mathrm{id}_{\mathrm{dom}(f)}$
$\underline{n+1}(f) = \underline{n}...
- 3,793
6
votes
1
answer
2k
views
Surreal numbers and large cardinals
This is a question in two parts about the interaction of surreal numbers and large cardinals, in both cases just a request for references on the subject.
Part 1 is about foundations. Much of the ...
- 4,907