Related papers: Brouwer and Cardinalities
This paper is the concise addition to the foregoing work "Inconsistency of Inaccessibility", containing the presentation of main theorem proof (in ZF) about inaccessible cardinals nonexistence. Here some refinement of this presentation is…
The paper is written for Kluwer's Encyclopaedia of Mathematics.
We construct a family F of compact and pathwise connected subsets of the Euclidean plane such that (i) the cardinality of F is that of the continuum (and hence extremely large) and (ii) if X,Y are distinct spaces in F then there never…
In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non-$T_1$ topological spaces using interval analysis. For a finite set with known cardinality, we give interval estimations based on the closure…
Let P be the direct product of countably many copies of the additive group Z of integers. We study, from a set-theoretic point of view, those subgroups of P for which all homomorphisms to Z annihilate all but finitely many of the standard…
Schanuel has pointed out that there are mathematically interesting categories whose relationship to the ring of integers is analogous to the relationship between the category of finite sets and the semi-ring of non-negative integers. Such…
Split preorders are preordering relations on a domain whose composition is defined in a particular way by splitting the domain into two disjoint subsets. These relations and the associated composition arise in categorial proof theory in…
We find the cardinality of the value sets of polynomial maps associated with simple complex Lie algebras $B_2$ and $G_2$ over finite fields. We achieve this by using a characterization of their fixed points in terms of sums of roots of…
A new generalization of the classical separate algebraicity theorem is suggested and proved.
Cameron-Liebler sets of subspaces in projective spaces were studied recently by Blokhuis, De Boeck and D'haeseleer (Des. Codes Cryptogr., 2019). In this paper, we discuss Cameron-Liebler sets in bilinear forms graphs, obtain several…
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
We introduce a natural two-cardinal version of Bagaria's sequence of derived topologies on ordinals. We prove that for our sequence of two-cardinal derived topologies, limit points of sets can be characterized in terms of a new iterated…
In this paper, we construct a differential graded Lie algebra whose Maurer-Cartan elements are given by crossed homomorphisms on Leibniz algebras. This allows us to define cohomology for a crossed homomorphism. Finally, we study linear…
We present several results concerning Shelah cardinals.
In this short note we will explore some recent connections between positivity, singularities, and boundedness in various contexts focusing on birational geometry.
In this paper, the notion of generic transversality and its characterization are given. The characterization is also a further improvement of the basic transversality result and its strengthening which was given by John Mather.
Using the formalism of polynomials with positive coefficients, the fact that exactly half of all subsets of a finite set have even cardinality can be generalized asymptotically.
Using the concept of constant evasion to different sorts of suitable binary relations, we establish many cardinal invariants derived from the established cardinal invariants $\mathfrak{e}^\mathrm{const}_{n}$ and…
In this talk, some aspects of duality symmetries are presented.
In this short note we present a class of conjectures on partitions of integers as summations of primes, which are extensions of Goldbach conjecture.