Related papers: Borel Determinacy: A Streamlined Proof
We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)
The Mordell conjecture: origins, approaches, generalizations -- The Mordell conjecture predicts that a diophantine equation defining a smooth projective curve of genus at least two has only finity many solutions in a given number field. The…
We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof…
The M-convexity of dual Schubert polynomials was first proven by Huh, Matherne, M\'esz\'aros, and St. Dizier in 2022. We give a full characterization of the supports of dual Schubert polynomials, which yields an elementary alternative proof…
We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017). This conjecture…
The paper contains a brief description of Yamasaki's remarkable investigation (1980) of the relationship between Moore-Yamasaki-Kharazishvili type measures and infinite powers of Borel diffused probability measures on ${\bf R}$. More…
In [10] the third author of this paper presented two conjectures on the additive decomposability of the sequence of ''smooth'' (or ''friable'') numbers. Elsholtz and Harper [4] proved (by using sieve methods) the second (less demanding)…
We update our paper: The collapse of Bell determinism (Physics Letters A, 359 (2006): 122-125; available online 16 June 2006). First, we point out that Olivier Brunet, using lattice theoretic methods, has recently, and quite independently,…
We present a selection of basic results on Borel reducibility of Borel ideals and equivalence relations, especially those with comparably short proofs. The focal point are reducibility/irreducibility results related to some special…
This paper gives bijective proofs of some novel coinversion identities first discovered by Ayyer, Mandelshtam, and Martin (arxiv:2011.06117) as part of their proof of a new combinatorial formula for the modified Macdonald polynomials…
In the present paper, a generalization of the first part of the Borel-Cantelli lemma is obtained by the recent work of Balakrishnan and Stepanov (2010). This generalization is further applied to derive strong limit results for the sequence…
The celebrated Mason's conjecture states that the sequence of independent set numbers of any matroid is log-concave, and even ultra log-concave. The strong form of Mason's conjecture was independently solved by Anari, Liu, Oveis Gharan and…
We generalize the recent results on radial projections by Orponen, Shmerkin, Wang using two different methods. In particular, we show that given $X,Y\subset \mathbb{R}^n$ Borel sets and $X\neq \emptyset$. If $\dim Y \in (k,k+1]$ for some…
In the previous author's paper the Macdonald norm conjecture (including the famous constant term conjecture) was proved. This paper contains the proof of the remaining two (the duality and evaluation conjectures). The evaluation theorem is…
We prove a conjecture of Stembridge concerning stability of Kronecker coefficients that vastly generalizes Murnaghan's theorem. The main idea is to identify the sequences of Kronecker coefficients in question with Hilbert functions of…
Recently, Colbeck and Renner (2011) [arXiv:1005.5173] published a theorem that appears to be stronger than the Bell (1964) theorem in a way that is more significant than the other variations of Bell's theorem that have been published in the…
We provide a simple proof of Tchakaloff's Theorem on the existence of cubature formulas of degree $m$ for Borel measures with moments up to order $m$. The result improves known results for non-compact supports, since we do not need…
The structure of the set of positivity-preserving maps between matrix algebras is notoriously difficult to describe. The notable exceptions are the results by St{\o}rmer and Woronowicz from 1960s and 1970s settling the low dimensional…
We aim to prove a twisted version of the Osborne conjecture obtained by Hecht and Schmid in their 1983 Acta Mathematica paper. Bergeron and Clozel (2013) have considered a special case, and we generalize their method to our setting.
We are concerned with the problem of witnessing the Baire property of the Borel and the projective sets (assuming determinacy) through a sufficiently definable function in the codes. We prove that in the case of projective sets it is…