Related papers: A continuation of [DjSh:691]
We give examples of $\mathrm{NIP}$ structures in which new algebraic structure appears in the Shelah completion. In particular we construct a weakly o-minimal structure $\mathscr{M}$ such that $\mathscr{M}$ does not interpret an infinite…
In this article, we derive meromorphic continuation of multiple Lerch zeta functions by generalising an elegant identity of Ramanujan. Further, we describe the set of all possible singularities of these functions. Finally, for the multiple…
Computations in the cohomology of finite groups.
We extend a recent result of Khalfalah and Szemeredi to the polynomials of prime variables.
Rejoinder to "The Future of Indirect Evidence" [arXiv:1012.1161]
We deal with (< kappa)-supported iterated forcing notions which are (E_0,E_1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the successor of a singular case. This continues…
This paper continues the development of the theory of finite localities that was begun in "Finite Localities I". The emphasis in this Part 2.
We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [8] holds while the classical Borel Conjecture fails.
We give an example of two $n\times n$ chess positions, $A$ and $B$, such that (1) there is a sequence $\sigma$ of legal chess moves leading from $A$ to $B$; (2) the length of $\sigma$ cannot be less than $\exp \Theta(n)$.
This note is a complement to an article which was published, six years ago, in The Ramanujan Journal (vol. 45.3, 2018). Here, the goal is to fully describe a singular transcendental continued fraction in Q((T^-1)), tied to a particular…
We comment on the results of the recent search by the LHCb collaboration for the doubly charmed baryon $\Xi_{cc}^+$.
We develop a theory of modulus triples, for future motivic applications.
We study the positivity of related cohomology classes concerning the convergence problem of inverse $\sigma_k$-flow in the conjecture proposed by Lejmi and Sz\'{e}kelyhidi.
Even though Zaremba's conjecture remains open, Bourgain and Kontorovich solved the problem for a full density subset. Nevertheless, there are only a handful of explicit sequences known to satisfy the strong version of the conjecture, all of…
We continue investigating rational quartic reciprocity laws and, at the suggestion of the editor of AA, provide details of a proof of a remark in the first article with this title.
Theory of $n$-complements with applications is presented.
Given an inaccessible J\'onsson cardinal $\lambda$, a sequence of results due to Shelah from Cardinal Arithmetic and Sh413 tell us that $\lambda$ must be at least $\lambda\times\omega$-Mahlo. We may then ask ourselves whether we can improve…
The star versions of the Scheepers property, namely star-Scheepers, strongly star-Scheepers and new star-Scheepers property have been introduced. We explore further ramifications concerning critical cardinalities. Quite a few interesting…
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
We give another proof of the second Rogers-Ramanujan identity by Kashiwara crystals.