Related papers: The iterability hierarchy above I3
We study the action of monads on categories equipped with several monoidal structures. We identify the structure and conditions that guarantee that the higher monoidal structure is inherited by the category of algebras over the monad.…
A novel higher-dimensional definition for Costas arrays is introduced. This definition works for arbitrary dimensions and avoids some limitations of previous definitions. Some non-existence results are presented for multidimensional Costas…
We prove that a universal class categorical in a high-enough cardinal is categorical on a tail of cardinals. As opposed to other results in the literature, we work in ZFC, do not require the categoricity cardinal to be a successor, do not…
Starting from the existence of many supercompact cardinals, we construct a model of ZFC in which the tree property holds at a countable segment of successor of singular cardinals.
Cicho\'n's diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and $\sigma$-compact subsets of the irrationals. It is consistent…
A set D of vertices of a graph G with vertex set V is irredundant if each non-isolated vertex of G[D] has a neighbour in V-D that is not adjacent to any other vertex in D. The upper irredundance number IR(G) is the largest cardinality of an…
We introduce a model of infinitary computation which enhances the infinite time Turing machine model slightly but in a natural way by giving the machines the capability of detecting cardinal stages of computation. The computational strength…
The work presents the brief exposition of the proof (in ZF) of inaccessible cardinals nonexistence. To this end in view there is used the apparatus of subinaccessible cardinals and its basic tools -- reduced formula spectra and matrices and…
We show that it is consistent that the continuum is as large as you wish, and for each uncountable cardinal $\kappa$ below the continuum, there are a subset $T$ of the reals and a family $A$ of countable subsets of $T$ such that (1) both…
We prove some consistency results about b(lambda) and d(lambda), which are natural generalisations of the cardinal invariants of the continuum b and d. We also define invariants b_cl(lambda) and d_cl(lambda), and prove that almost always…
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…
In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.
We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obtain an extension universe with morasses at every regular…
Let $\kappa$ be any regular cardinal. Assuming the existence of a huge cardinal above $\kappa$, we prove the consistency of $\binom{\kappa^{++}}{\kappa^+}\rightarrow\binom{\tau}{\kappa^+}$ for every ordinal $\tau<\kappa^{++}$. Likewise, we…
New (infinitely many) rational approximants to \zeta(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A…
We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting.
This document contains additional experiments concerned with the evaluation of the Hierarchical Subspace Iteration Method, which is introduced in~\cite{Nasikun2021}}
We prove two general results about the preservation of extendible and $C^{(n)}$-extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vop\v{e}nka's…
Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's…
Let $R$ be a formal power series ring over a field, with maximal ideal $\mathfrak m$, and let $I$ be an ideal of $R$ such that $R/I$ is Artinian. We study the iterated socles of $I$, that is the ideals which are defined as the largest ideal…