Related papers: On the Isbell problem

Any refinement system (= functor) has a fully faithful representation in the refinement system of presheaves, by interpreting types as relative slice categories, and refinement types as presheaves over those categories. Motivated by an…

We construct uncountably many discrete groups of type $FP$; in particular we construct groups of type $FP$ that do not embed in any finitely presented group. We compute the ordinary, $\ell^2$- and compactly-supported cohomology of these…

Using a fully connected feedforward neural network we study topological invariants of a class of Calabi--Yau manifolds constructed as hypersurfaces in toric varieties associated with reflexive polytopes from the Kreuzer--Skarke database. In…

We outline a method for constructing effectively two-dimensional isotropic optical media that are perfectly and omnidirectionally invisible for both TE and TM waves provided that their wavenumber does not exceed a preassigned value…

For which (first-order complete, usually countable) $T$ do there exist non-isomorphic models of $T$ which become isomorphic after forcing with a forcing notion $\mathbb{P}$? Necessarily, $\mathbb{P}$ is non-trivial; i.e.~it adds some new…

We describe forms with non-Abelian charges. We avoid the use of theories with flat curvatures by working in the context of topological field theory. We obtain TQFTs for a form and its dual. We leave open the question of getting gauges in…

We obtain a forcing construction that shows that it is consistent that the torsion-free Abelian group $\mathbb{Q}^{(\lambda)}$ admits a Hausdorff group topology which is also $\mathcal{U}$-compact and contains no non-trivial convergent…

We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…

We model the environment of eukaryotic nuclei by representing macromolecules by only their entropic properties, with globular molecules represented by spherical colloids and flexible molecules by polymers. We put particular focus on…

For ultrafilters u,v on N, the operation u/v is introduced and formalised which acts as quotient-like structures when v strongly divides u.Central to our study is the characterization of self-divisible ultrafilters in connection with the…

Currently the two popular ways to practice Robinson's nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions…

In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the…

We refine and generalize the results of K. E. Lauter and E. W. Howe on principal polarizations on products of abelian varieties over finite fields. Firstly, we study the reasons for the absence of an irreducible principal polarization in…

We prove the undecidability of the third order pattern matching problem in typed lambda-calculi with dependent types and in those with type constructors by reducing the second order unification problem to them.

In \cite{HK}, Hayut and Karagila asked some questions about uniform ultrafilters in a choiceless context. We provide several answers to their questions.

Theorem: There is a {\em complete sentence} $\phi$ of $L_{\omega_1,\omega}$ such that $\phi$ has maximal models in a set of cardinals $\lambda$ that is cofinal in the first measurable $\mu$ while $\phi$ has no maximal models in any $\chi…

Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…

This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, inductive limit group, Zariski topology and the dimension of the…

We construct a family of n+1 dyadic filtrations in R^n, so that every Euclidean ball B is contained in some cube Q of our family satisfying diam(Q) \le c_n diam(B) for some dimensional constant c_n. Our dyadic covering is optimal on the…

A model with a sequence of indiscernibles depending on a particular precovering set is constructed.The initial assumption is as follows: for every n<omega the set {alpha | o(alpha)=alpha^+n } is unbounded in kappa.