Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with set-theory
Search options not deleted
user 1610
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
3
votes
Explicitly constructing an infinite set with particular size
As others have already noted, the notion of size these algorithms appeal to is not the cardinality of a set.
However, there is a useful sense in which your intuition can be formalized: via the ordin …
- 9,201
5
votes
Set-theoretic foundations for formal language theory?
Hi Anthony,
The question you're asking in your text isn't quite the same as the question in your title, but the answer to the title subsumes the one you ask in the text.
To define a grammar, we st …
- 9,201
1
vote
Dispensing with the notion of infinity for the sake of coverings
I don't quite know what you mean by "coverings of topology", but it is possible to formalize a notion of size for infinite sets which relies on the part-whole conception, rather than the bijective cor …
- 9,201
7
votes
Can we prove set theory is consistent?
Is there any reason to believe that Set1 cannot prove the consistence of Set2? Or I'm just confused and what I said does not make sense?
What you're asking does make sense, but there are good inf …
- 9,201
16
votes
Accepted
Is there a category of non-well-founded sets?
Yes, there is. See Peter Aczel's 1988 notes on models of non-well-founded set theory, here. The basic idea is that you can model sets as graphs (ie, as a collection of element sets together with a bin …
- 9,201
18
votes
Can we disallow finite choice?
This is possible in constructive mathematics, because it distinguishes between finite sets and sets with a counted number of elements. (I'm not quite sure what the standard terminology is, though.)
A …
- 9,201
10
votes
Were Bourbaki committed to set-theoretical reductionism?
The difficulties in formalizing categorical reasoning in set theory are actually pretty simple to understand -- it's just an annoying incompatibility in how the notion of size is used in practice in c …
- 9,201
12
votes
Uses of bisimulation outside of computer science.
As you probably know, between choice and foundation, any use of coinductive arguments in ZFC can be eliminated. So you often have cases where coinduction could have been used, but more inductive metho …
- 9,201
6
votes
Accepted
Examples of inductive proofs that can be generalized by transfinite induction
A nice example arises in structural proof theory. You can prove cut-elimination of the sequent calculus for first-order logic by an induction on the size of the cut formula, and the sizes of the proof …
5
votes
Are there nonequivalent randomnesses?
First, there's a difference between Kolmogorov probability and Bayesian probability theory. The Kolmogorov axioms require countable additivity, which Bayesians have difficulty justifying, for a variet …
- 9,201
16
votes
Logic in mathematics and philosophy
I agree with Timothy and Andrej's answers, and will complement them by suggesting a few books by philosophers and philosophically-inclined logicians which I have found very interesting. I am sure the …
- 9,201