Related papers: Remarks on an article by Rabern et al
This is a sequel to the author's "Truth and Knowledge", College Publications, 2022, and contains some problems and results in connection with a possible representation for Yablo like structures.
In this short paper, I present a few theorems on sentences of arithmetic which are related to Yablo's Paradox as G\"odel's first undecidable sentence was related to the Liar paradox. In particular, I consider two different arithemetizations…
The article presents the proof of Casas-Alvero conjecture.
A conjecture regarding the structure of expander graphs is discussed.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
We suggest a forcing version of Yablo's paradox and discuss its implication on self-reference.
I reply to the four points raised by S. A. Hayward, R. Di Criscienzo, M. Nadalini, L. Vanzo, S. Zerbini (arXiv:0909.2956v1) against my comment (arXiv:0907.2020v1) to their previous article. I maintain my position on the wrongness of their…
The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open…
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
Khabibullin's conjecture has three statements equivalent to each other. Recently Ruslan Sharipov has constructed a counterexample to this conjecture for one of its three statements. In this paper Sharipov's counterexample is transferred to…
We point out a mistake in the statement of Corollary 2 in R. C. Alperin's paper on Selberg's lemma.
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
In this paper, we state the validity of Cramer's rule in a tropical context and its correspondence with classical Cramer's rule. This correspondence will allow us to prove a constructive version of Pappus' theorem conjectured in the paper…
We present a counter example to a theorem given by Amir {\em et al.} J. Math. Phys. {\bf 35}, 3005 (1994). We also comment on a misleading statements of the same reference.
We discuss the towers of finite \'etale covers which were essentially introduced by A.Tamagawa. The statement about correspondence between sections and cofinal towers is a folklore but perhaps not in a very explicit form. The last section…
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
We prove a conjecture of Johann Cigler on shifted Hankel determinants.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
The aim of this paper is to study a conjecture predicting a lower bound on the canonical height on abelian varieties, formulated by S. Lang and generalized by J. H. Silverman. We give here an asymptotic result on the height of Heegner…