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Results tagged with reference-request
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user 12978
This tag is used if a reference is needed in a paper or textbook on a specific result.
4
votes
Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prer...
As for your question on prerequisites, the more logic you know the better. Of course the basic concepts---proofs, models, Peano arithmetic, incompleteness, compactness, nonstandard models, primitive …
- 6,287
13
votes
1
answer
3k
views
Does this metric have an official name? Lévy metric? Ky Fan metric?
Let $X$ and $Y$ be random variables taking values in a separable metric space $(S,d)$. The metric I have in mind is
$$\rho(X,Y) = \mathbb{E}[\min\{d(X,Y),1\}]$$
if $X$ and $Y$ take values in the a me …
- 111
8
votes
Accepted
Computing the complex roots of a monic polynomial
I'm worried that I'm misunderstanding your question, but I think one could argue there is no satisfactory answer here except to say that this result likely predates "computability" itself.
From the wi …
- 6,287
7
votes
Good introductory book to type theory?
If your interest is type theoretic foundations, you might want to look into modern (type-theory based) theorem provers. This is how I learned both type theory and dependent type theory. This has the …
- 6,287
9
votes
2
answers
535
views
What mode of convergence is this?
I'm interested in a new (to me) mode of convergence which is stronger than convergence in measure/probability. I want to know if it has a name and if it is used much in the literature. I will write …
CommunityBot
- 1
3
votes
1
answer
274
views
What is the extension of the truth-table degrees to Baire Space called?
Recall that for sets $A, B \in 2^\omega$ that we say $A \leq_{tt} B$ if there is a total Turing functional $F \colon 2^\omega \to 2^\omega$ such that $F(B)=A$. This is called truth-table reducibility …
- 48.8k
6
votes
The unpublished papers in reference to the published papers
As the reader, you can also ask mathoverflow for help finding the paper. There have been some very interesting MO questions along this line. In particular, this record helps others to also track dow …
CommunityBot
- 1
6
votes
Accepted
Formal definition of arithmetic transfinite recursion
To repeat Emil and Andreas's comments, it can be found in Stephen G. Simpson, "Systems of Second-Order Arithmetic", the first chapter of which is available here:
http://www.personal.psu.edu/t20/sosoa …
- 6,287
6
votes
Accepted
Recent trends in effective analysis
(At François's request, my comment in now an answer.)
Yes, it is still an active research area. It however is spread out throughout a number of camps (traditions): The Weihrauch camp, the reverse mat …
- 6,287
1
vote
0
answers
1k
views
What conditions on a filtration guarantee that a (sub)martingale has a continuous modification?
There is a theorem as follows:
Theorem. Let $\mathcal{F}_t$ be a filtration which is right-continuous and complete. Assume $M_t$ is a submartingale adapted to $\mathcal{F}_t$ such that $t \mapsto \m …
CommunityBot
- 1
7
votes
1
answer
389
views
Reference request: Martingale decompositions (positive/negative and u.i./singular)
For a paper I am writing, I need these two facts. The proofs are fairly short, but I would rather just cite them. This is for martingales index by natural numbers. Also, I call a martingale which co …
CommunityBot
- 1