相关论文: A constructive proof of a theorem by Ferreira-Zant…

This expository note presents a constructive proof of Wigner's theorem using only a few basic facts about Hilbert spaces, such as the existence of orthonormal bases and the Fourier decomposition of a vector. Our proof is based on a proof by…

We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.

In this paper, we present a constructive proof of Herschfeld's Convergence Theorem. Our formulation differs from Herschfeld's in a few ways: We consider radicals that nest transfinitely many times, as these are essential to the proof;…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

The paper presents a new proof of O'Cinneide's characterization theorem. It is much simpler than the original one and constructive in the sense that we not only show the existence of a phase type representation, but present a procedure…

Recently, Artemov [4] offered the notion of constructive consistency for Peano Arithmetic and generalized it to constructive truth and falsity in the spirit of Brouwer-Heyting-Kolmogorov semantics and its formalization, the Logic of Proofs.…

A C.R. note by Alano Ancona from 1980 is reexamined. Within his line of ideas in the proof two new theorems are constructed. No claim of originality. These are put into the context of later research. One far reaching conjecture is given.…

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.

We discuss some highlights of our computer-verified proof of the construction, given a countable transitive set-model $M$ of $\mathit{ZFC}$, of generic extensions satisfying $\mathit{ZFC}+\neg\mathit{CH}$ and $\mathit{ZFC}+\mathit{CH}$.…

The Furstenberg-Zimmer structure theorem for $\mathbb{Z}^d$ actions says that every measure-preserving system can be decomposed into a tower of primitive extensions. Furstenberg and Katznelson used this analysis to prove the…

An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…

The proof of Theorem 11 of the paper M. Scheepers, Remarks on countable tightness, Topology and its Applications 161 (2014), 407 - 432 relies on Lemma 10 of that paper. The offered proof of Lemma 10 had shortcomings, and I was recently…

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

If the sequent (Gamma entails forall x exists y A) is provable in first order constructive natural deduction, then the theory (Gamma, forall x (f (x)/y)A), where f is a new function symbol, is a conservative extension of Gamma.

An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory…

A constructive and straightforward proof of the existence of the Zeeman topology is provided, contradicting a fallacious claim contained in the paper "Does Zeeman's Fine Topology Exist?" available at arXiv:1003.3703v1.

The Farkas lemma is proved and applied to obtain a structure theorem for polyhedra. These notes are based on a talk in the New York Number Theory Seminar on October, 20, 2022.

We present a very simple example of a theorem with constructive and non-constructive proofs: the equation c^2 x^2 - (c^2 + c)x + c = 0 has a solution.