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Proof of second incompleteness theorem for Set theory without Arithmetization of Syntax

Is there a proof of the second incompleteness theorem of Godel for set theory which doesn't use Arithmetization of Syntax (Godel numbering)? I came across a short proof by Thomas...

Asked on 12/18/2021

0 answer

Characterization of effective descent morphism

A faithfully flat morphism of commutative rings $A rightarrow B$ is an effective descent morphism. So is a regular monomorphism (right?). What is a characterization of...

Asked on 12/18/2021 by Kind Bubble

0 answer

Analogue of decay of Fourier coefficients of a smooth function on $mathbb{S}^1$

Let $nu$ be the uniform measure on the unit circle $mathbb{S}^1 subset mathbb{R}^2$, normalised so that $nu(mathbb{S}^1) = 1$. Suppose $mu$ is a Borel probability measure...

Asked on 12/18/2021

2 answer

Strong Data Processing Inequality for capped channels

Let $X$ and $Y$ be two $rho$ correlated Gaussian vectors, such that $X,Ysim N(0,1)^n$ and $E[X_iY_i]=rho$.Let $M_X = f(X)$ and $M_Y =...

Asked on 12/18/2021 by Thomas Dybdahl Ahle

1 answer

lattice suprema vs pointwise suprema

What is the difference between the lattice supremum and the pointwise supremum of a family of functions? I mean, given a family of real valued functions $mathcal{F}$, is the...

Asked on 12/18/2021 by Giuliosky

2 answer

In infinite dimensions, is it possible that convergence of distances to a sequence always implies convergence of that sequence?

This is a cross-posted on MSE here. Let $(X,d)$ be a metric space. Say that $x_nin X$ is a P-sequence if $lim_{nrightarrowinfty}d(x_n,y)$ converges for every ...

Asked on 12/18/2021

2 answer

Are those distributional solutions that are functions, the same as weak solutions?

There are two closely related concepts and I am not sure exactly how close. Consider a partial differential equation. (The coefficients need not be constant but assume they...

Asked on 12/18/2021

0 answer

Ability to have function sequence converging to zero at some points

Consider the continuous and non negative function $c : mathbb R to [0,1]$ defined by $$c(x) = begin{cases}cos frac{pi x}{2} &text{for } x in [-1,1]\0 &text{otherwise}end{cases}$$...

Asked on 12/16/2021 by mathcounterexamples.net

1 answer

Curious anti-commutative ring

Has anyone seen the ring $Lambda[x_0, x_1, x_2, ldots]/(x_i x_j - (i+1) x_0 x_{i+j})$ in some natural context? Here $Lambda[x_0, x_1, x_2, ldots]$ is the (graded-)commutative algebra (either...

Asked on 12/16/2021 by Robert Bruner

1 answer

Minkowski (box-counting) dimension of generalized Cantor set

I'm trying to solve this problem.For $0<alpha, beta<1,$ let $K_{alpha, beta}$ be the Cantor set obtained as an intersection of the following nested compact sets. $K_{alpha, beta}^{0}=[0,1]...

Asked on 12/16/2021

0 answer

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