Logic Papers of the Week

For 𝑟 = 2 after decades of effort, a complete solution was given by the Complete Intersection Theorem ([2]).

``Emergence'' refers to the fact that different mathematical languages and theories seem to be required to describe scientific theories that operate at different spatial and temporal scales.

We prove that every monadically dependent graph class has almost bounded merge-width, thereby confirming a conjecture of the first and the last author [STOC '25].

In particular, we show that in monadically dependent classes, tuples of fixed length have only $|U|^{O(1)}$ types of fixed quantifier rank over any set of parameters $U$.

The 1-2-3 Conjecture asserts that every finite graph without isolated edges admits edge weights from $\{1,2,3\}$ such that the sum function forms a vertex coloring. We study its Borel analogue for locally finite Borel graphs without isolated edges, proving that five weights suffice in general and four suffice for regular graphs.

In this study, some types of convexity, like strictly (strongly) convexity, (λ,ψ)-convexity with different senses over fuzzy soft expert set, have been described with the numerical examples.

We provide quantitative results on the asymptotic behavior of Dykstra’s algorithm with Bregman projections, a combination of the well-known Dykstra’s algorithm and the method of cyclic Bregman projections, designed to find best approximations and solve the convex feasibility problem in a non-orthogonal setting.

It remains unclear why individuals are susceptible to such content, especially in contexts featuring social engagement cues. Therefore, this study aims to investigate the roles of multimodality, online comments and virality metrics in disinformation evaluation.

We prove that the family of coset relations of $F_\sigma$ real linear subspaces of Banach space $\ell_1$ has no common upper bound among Borel equivalence relations in the sense of Borel reducibility.

We construct a counterexample in one fixed countable language.

We study the relationship between large cardinals and Blass' Small Violation of Choice ($\mathsf{SVC}$), which states that the Axiom of Choice holds in a set-generic extension of the universe.

In this paper, we investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure.

In this paper, we establish an analogue for lovely pairs of pseudofinite fields.

This paper develops dynamic set theory, which adds natural time to sets from the perspective of human perception.

A bibliometric analysis of multi-criteria decision-making (MCDM) studies was conducted using 8,947 articles published between 1995 and 2025.

We characterize the uniform computational strength of finding one-way Eulerian paths in countable graphs.

We introduce a combinatorial principle $\textsf{SC}(\kappa)$, for any regular cardinal $\kappa \ge \omega_2$, which asserts the existence of a family $\mathcal{Y} \subseteq [H(\kappa)]^\omega$ of elementary substructures of $H(\kappa)$ which is closed under finite intersections and satisfies that for stationarily many $N \in \mathcal{Y}$, if $M \in \mathcal{Y}$ and $M \cap \omega_1 < N \cap \omega_1$, then $M \cap N \cap \kappa \in N$.

We prove equivalences of asymmetric partition relations involving natural numbers and products of weakly compact cardinals $\kappa$, infinite cardinals $\lambda<\kappa$ and natural numbers to certain classes of finitary problems in the theory of edge-coloured digraphs.

We study the relation between the existence of escaping (or hyperimmune) functions and weak 1-genericity using computability over ideals.

The aim of this paper is to show how infinitary logic can be used to lift model-theoretic results in arithmetic to a quantifier-sensitive form.