相关论文: A Power Function with A Fixed Finite Gap Everywher…
A ccc-generically supercompact cardinal $\kappa$ can be smaller than or equal to the continuum. On the other hand, such a cardinal $\kappa$ still satisfies diverse largeness properties, like that it is a stationary limit of ccc-generically…
We determine the diameter of every connected component of the complement of the power graph and the enhanced power graph of a finite group, which completely answers two questions by Peter J. Cameron.
We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number $r \in \{1\} \cup [2, \infty)$, positive semi-definite matrices $A_i,\…
Using a theorem from pcf theory, we show that for any singular cardinal nu, the product of the Cohen forcing notions on kappa, kappa < nu adds a generic for the Cohen forcing notion on nu^+. This solves Problem 5.1 in Miller's list…
Recently the second author introduced combinatorial principles that characterize supercompactness for inaccessible cardinals but can also hold true for small cardinals. We prove that the proper forcing axiom PFA implies these principles…
In this paper we investigate more characterizations and applications of $\delta$-strongly compact cardinals. We show that, for a cardinal $\kappa$ the following are equivalent: (1) $\kappa$ is $\delta$-strongly compact, (2) For every…
In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…
Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we…
This paper explores several topics related to Woodin's HOD conjecture. We improve the large cardinal hypothesis of Woodin's HOD dichotomy theorem from an extendible cardinal to a strongly compact cardinal. We show that assuming there is a…
I introduce a new family of axioms extending ZFC set theory, the $\Sigma_n$-correct forcing axioms. These assert roughly that whenever a forcing name $\dot{a}$ can be forced by a poset in some forcing class $\Gamma$ to have some $\Sigma_n$…
From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact cardinal kappa is fully indestructible by kappa-directed…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions are extremely important for some reasons. First, its…
V\"a\"an\"anen and Welch asked in the paper "When cardinals determine the power set: inner models and H\"artig quantifier logic" which large cardinals are consistent with the power set operation $x\mapsto P(x)$ being $\Sigma_1$-definable in…
We make use of some observations on the core model, for example assuming $V=L [ E ]$, and that there is no inner model with a Woodin cardinal, and $M$ is an inner model with the same cardinals as $V$, then $V=M$. We conclude in this latter…
In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…
The inner model problem for supercompact cardinals, one of the central open problems in modern set theory, asks whether there is a canonical model of set theory with a supercompact cardinal. The problem is closely related to the more…
We define forcing orders which add witnesses to the failure of various forms of Friedman's Property. These posets behave similarly to the forcing order adding a nonreflecting stationary set but have the advantage of allowing the…
In this work we discuss the exact solution to the algebraic equation associated to the Ricci tensor in the quadratic $f(R,Q)$ extension of Palatini gravity. We show that an exact solution always exists, and in the general case it can be…
We prove some distribution results for the $k$-fold divisor function in arithmetic progressions to moduli that exceed the square-root of length $X$ of the sum, with appropriate constrains and averaging on the moduli, saving a power of $X$…