Related papers: Weihrauch goes Brouwerian

We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion ($\mathsf{ATR}_0$) from the point of view of computability-theoretic reducibilities, in particular Weihrauch…

We prove a polynomial bound in the "true complexity" problem of Gowers and Wolf. The proof uses only repeated applications of the Cauchy--Schwarz inequality, answering negatively a question posed by Gowers and Wolf. To choose and reason…

We prove that a finite dimensional algebra $\Lambda$ is $\tau-$tilting finite if and only if all the bricks over $\Lambda$ are finitely generated. This is obtained as a consequence of the existence of proper locally maximal torsion classes…

The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is…

There are two possible computational interpretations of second-order arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a…

This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…

We study the periplectic Brauer algebra introduced by Moon in the study of invariant theory for periplectic Lie superalgebras. We determine when the algebra is quasi-hereditary and, for fields of characteristic zero, describe the block…

In 1952, Michael posed a question about the functional continuity of commutative Frechet algebras in his memoir, known as Michael problem in the literature. We settle this in the affirmative along with its various equivalent forms, even for…

In this paper, we investigate the many-valued version of coalgebraic modal logic through predicate lifting approach. Coalgebras, understood as generic transition systems, can serve as semantic structures for various kinds of modal logics. A…

Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…

Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…

To a finite group G one can associate a tower of wreath products S_n[G]. It is well known that the graded direct sum of the Grothendieck groups of the categories of finite dimensional complex representations of these groups can be given the…

We introduce Bifurcation Logic, BL, which combines a basic classical modality with separating conjunction * together with its naturally associated multiplicative implication, that is defined using the modal ordering. Specifically, a formula…

In this paper we establish a connection between ribbon graphs and Brauer graphs. As a result, we show that a compact oriented surface with marked points gives rise to a unique Brauer graph algebra up to derived equivalence. In the case of a…

A classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial…

In this work we study the notions of structural and universal completeness both from the algebraic and logical point of view. In particular, we provide new algebraic characterizations of quasivarieties that are actively and passively…

We realize (via an explicit isomorphism) the walled Brauer algebra for an arbitrary integral parameter delta as an idempotent truncation of a level two cyclotomic degenerate affine walled Brauer algebra. The latter arises naturally in Lie…

We define and study an alternative partial order, called the spectral order, on a synaptic algebra-a generalization of the self-adjoint part of a von Neumann algebra. We prove that if the synaptic algebra A is norm complete (a Banach…

In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…

We construct a quadratic basis of generators of matrix-extended $\mathcal{W}_{1+\infty}$ using a generalization of the Miura transformation. This makes it possible to conjecture a closed-form formula for the operator product expansions…