All Questions
Tagged with set-theory soft-question
16 questions with no upvoted or accepted answers
19
votes
0
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905
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What examples of existence forcing proofs are there?
Forcing proofs tend to be fairly constructive, in the sense that if I claim that there is a forcing that does something, I usually prove this by constructing that forcing.
There are only a handful of ...
- 39.8k
8
votes
0
answers
187
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Intuition for branch uniqueness in inner model theory
In inner model theory, what is the intuition behind the expectation that under appropriate conditions, we should have a single preferred branch to continue an iteration at a limit stage?
At the level ...
- 7,545
8
votes
0
answers
682
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Is there any theorem achieving Conway's "Mathematician's Liberation Movement"
John Conway on in the appendix to part zero of ONAG describes a "Mathematician's Liberation Movement". The goal would be to give mathematicians the freedom to create mathematical theories with the ...
- 6,353
8
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0
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172
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Sharply less regular cardinals in set theory
If $\lambda<\kappa$ are two regular cardinals, then every locally $\lambda$-presentable category is locally $\kappa$-presentable. The analogous statement does not hold for $\lambda$-accessible ...
- 5,482
8
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0
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1k
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What's Reeb's take on naive integers?
Georges Reeb's "claim Q" is the statement that "naive integers don't fill up $\mathbb{N}$". To anyone familiar with model theory this could easily be interpreted as the existence of nonstandard models ...
- 16.6k
4
votes
0
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333
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Is this result of Hajnal and Juhász correct?
I am having some trouble with the following result presented here:
Obviously I'm missing something, but I think from that result it could be shown that if $X$ is an infinite topological space, then $...
- 674
3
votes
0
answers
125
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Understanding the Relationship Between ω-Categories and (∞,1)-Categories
I've been reading about higher category theory and am curious about the distinctions and relationships between ω-categories and (∞,1)-categories. Specifically, I have the following questions:
...
- 441
3
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0
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342
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A Question Regarding Boolean-valued Models
What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. There also seems to ...
- 6,132
2
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0
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342
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What's the definition of a mouse in Mitchell's handbook article "the covering lemma"?
In the book "handbook of set theory", in the chapter "the covering lemma", definition 3.24, Mitchell defines what is mouse.
However he did not give any definition of $\mathcal{U}_\...
- 1,490
2
votes
0
answers
186
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Are there some algorithms which have high consistency strength?
Are there some algorithms, their time complexity is relatively good, for example polynomial time.
And the correctness of them has high consistency strength.
And these algorithms shouldn't able to ...
- 1,490
2
votes
0
answers
371
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Descriptive set theory on $\mathbb{R}^\mathbb{N}$
The short version of my question is, What is a good source for learning about descriptive set theory on the space $\mathbb{R}^\mathbb{N}$, under the product topology coming from the discrete topology ...
- 20.5k
1
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0
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266
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Is Jensen's covering lemma meaningful in a platonist's view?
The typical applications of fine structure theory are finding out the lower bounds of consistency strength of axiom systems. In such a proccess, we also constructs many combinatorial objects in core ...
- 1,490
1
vote
0
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170
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Can Jensen's covering lemma be proven easier in generic extensions of L?
Jensen's covering lemma, stating that if there is no $0^\#$ in V, then some covering property holds true, has a very complex proof.
In any generic extension L[G] of L, $0^\#$ don't exist, so the ...
- 1,490
1
vote
0
answers
268
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The most simple proof of projective determinacy
I want to read the proof of projective determinacy.
But every proof I could find (martin-steel original, koepke's, the proof in schindler's book, martin's new book) is too long.
Are there a simple ...
- 1,490
1
vote
0
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223
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What should one know about abstract sets and structural foundations?
Recently I came by accident across the book sets for mathematics by Lawvere. It says:
First we deplete the object of nearly all content. We could think of an idealized
computer memory bank that ...
0
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0
answers
416
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Solving the equation $\operatorname{Powerset}(X)=\varnothing$
There are (at least) two variants of this question.
Is it possible to modify the axioms of set theory, without arriving at obvious contradiction, in such a way that in a model of the theory there is ...
- 18.4k