All Questions
Tagged with set-theory foundations
157 questions
74
votes
11
answers
12k
views
Why hasn't mereology succeeded as an alternative to set theory?
I have recently run into this Wikipedia article on mereology. I was surprised I had never heard of it before and indeed it seems to be seldom mentioned in the mathematical literature. Unlike set ...
- 5,902
11
votes
3
answers
2k
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Kunen's use of Countable Transitive Models
Hi,
I have a doubt concerning Kunen's exposition of forcing in his classical book (arguably $the$ book on forcing). When dealing with Countable Transitive Models to set up the forcing machinery, ...
8
votes
2
answers
863
views
Consistent hierarchy of axiomatic systems
First of all, I am not an expert in model theory. I just want to get my personal view on the foundations of mathematics straight.
I just learned in Sergey Melikhov's answer to another question ...
- 25.5k
5
votes
5
answers
1k
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Concrete models of abstract structures
Most mathematicians seem to be contented with the fact, that abstract structures cannot be directly modelled as such in a set theory without ur-elements. What seems to me the standard stance: Set ...
- 9,720
5
votes
4
answers
2k
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Subsystems of Peano arithmetic and incompleteness theorem
I think everyone is familiar with Goedel's incompleteness theorems. In particular they imply that PA (Peano arithmetic) can not prove its own consistency. Now my question is what is the largest ...
- 741
2
votes
0
answers
167
views
Multitype approaches to choice?
I wonder if anyone has developed a set theory which approaches the issue of the non-emptiness of products of non-empty sets via a hierarchy of types (comparable to how Von Neumann–Bernays–Gödel set ...
- 17.6k
17
votes
10
answers
7k
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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 ...
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