Related papers: The comparability numbers and the incomparability …

In this letter we study a class of symmetries of the new translational extended shape invariant potentials. It is proved that a generalization of a compatibility condition introduced in a previous article is equivalent to the usual shape…

We introduce and prove the consistency of a new set theoretic axiom we call the \emph{Invariant Ideal Axiom}. The axiom enables us to provide (consistently) a full topological classification of countable sequential groups, as well as fully…

We introduce a stronger version of an $\omega_1$-guessing model, which we call an indestructibly $\omega_1$-guessing model. The principle IGMP states that there are stationarily many indestructibly $\omega_1$-guessing models. This…

This paper addresses the longstanding problem of determining the structure of the $\leq_{\mathrm{LT}}$-order in the Effective Topos, known to effectively embed the Turing degrees. In a surprising discovery, we show that the…

We establish a bijection between the set of finite topological $T_0$-spaces (or partially ordered sets) and equivalence classes of square matrices. The absolute value of the determinant or the rank of these matrices serve as simple homotopy…

Using the Rost invariant for non split simply connected groups, we define a relative degree $3$ cohomological invariant for pairs of orthogonal or unitary involutions having isomorphic Clifford or discriminant algebras. The main purpose of…

We work with the *-product introduced in [GHK25] and f-generic types to describe the minimal ideals of invariant types and to classify ergodic Keisler measures in amenable NIP theories. Moreover, we analyze the situation around the…

For any finitely generated module $M$ with non-zero rank over a commutative one-dimensional Noetherian local domain, we study a numerical invariant $\operatorname{h}(M)$ based on a partial trace ideal of $M$. We study its properties and…

In this paper, based mainly on the method of Iwasawa and Kida, by studying in detail the Hasse units and the ramifications of prime ideals, we obtain explicit results of Iwasawa invariants $ \lambda_{2} $ of the cyclotomic $…

In this paper, we study various factorization invariants of arithmetical congruence monoids. The invariants we investigate are the catenary degree, a measure of the maximum distance between any two factorizations of the same element, the…

Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring…

In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.

We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…

Given finite posets $P$ and $Q$, we consider a specific ideal $L(P,Q)$, whose minimal monomial generators correspond to order-preserving maps $\phi:P\rightarrow Q$. We study algebraic invariants of those ideals. In particular, sharp lower…

We study several ideal-based constructions in the context of singular stationarity. By combining methods of strong ideals, supercompact embeddings, and Prikry-type posets, we obtain three consistency results concerning mutually stationary…

In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive…

For a free ultrafilter U on omega we study several cardinal characteristics which describe part of the combinatorial structure of U. We provide various consistency results; e.g. we show how to force simultaneously many characters and many…

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

In this paper, we study some new examples of ideals on $\omega$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order -- known as the…

We introduce the property ``$F$-linked'' of subsets of posets for a given free filter $F$ on the natural numbers, and define the properties ``$\mu$-$F$-linked'' and ``$\theta$-$F$-Knaster'' for posets in a natural way. We show that…