Related papers: Reflection theorems for number rings
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
This expository and review paper deals with the Diamond Lemma for ring theory, which is proved in the first section of G. M. Bergman, The Diamond Lemma for Ring Theory, Advances in Mathematics, 29 (1978), pp. 178-218. No originality of the…
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
The content of this preprint together with additional material appears now in 0706.2154.
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
In the Letter 'Comment on 'Affine density, von Neumann dimension and a problem of Perelomov', arXiv.2211.04879, by Prof. J. L. Romero, it is claimed that the main theorem of Ref2 := [Adv. Math. 407, Article ID 108564, 22 p. (2022)] is…
This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2073.
The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…
We point out that the main theorem of Ref2 := [Adv. Math. 407, Article ID 108564, 22 p. (2022)] is included in the prior research survey Ref1 := [Expo. Math., 40(2), 265-301, 2022]. For context, we also reproduce the rather simple proof…
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…
We prove that cancellation of reflexive modules over affine rings holds under some restrictions. We construct examples to show that this is false even over polynomial rings without the extra assumptions.
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
The present preprint completes the arXiv preprint #2202.11652, entitled "Pseudodifferential arithmetic and the Riemann hypothesis", devoted to a proof of the conjecture. The first 4 pages of that preprint were devoted to a set of necessary…
The author decided to withdraw this paper by 1) an error in Lemma 5.11 (and 5.12) which requires some justification; 2) the main result of this paper suffers overlap with arXiv:1203.5254; 3) the author decided to split arXiv:1203.5254 into…
Extending Aanderaa's classical result that $\pi^1_1<\sigma^1_1$, we determine the order between any two patterns of iterated $\Sigma^1_1$- and $\Pi^1_1$-reflection. We show that this \emph{linear reflection order} is a prewellordering of…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
This paper ("Two-Level Chromophore and Irreversibility", which can be found at arXiv:0804.0086) has been withdrawn by the author due to too many errors and misleading statements. This paper has been superseded by Section 2.11 and Chapter 7…
The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the…
This preprint has been withdrawn. It is because I will never publish this preprint since everything has been contained in my new preprint: arXiv:0907.1506. Please refer to arXiv:0907.1506. Please do not cite this preprint any more.