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pro vyhledávání: '"Veldman, Wim"'
Autor:
Veldman, Wim
We discuss the position of intuitionistic mathematics within the field of constructive mathematics. We discuss some principles defended and used by Brouwer but rejected by Bishop, like the Coninuity Principle, the Fan Theorem and the Bar Theorem. We
Externí odkaz:
http://arxiv.org/abs/2202.06078
Autor:
Veldman, Wim
The paper is an introduction to intuitionistic mathematics.
Externí odkaz:
http://arxiv.org/abs/2102.01561
Autor:
Veldman, Wim
We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.
Externí odkaz:
http://arxiv.org/abs/1911.09477
Akademický článek
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Autor:
Veldman, Wim
We prove intuitionistic versions of the classical theorems saying that all countable closed subsets of $[-\pi,\pi]$ and even all countable subsets of $[-\pi,\pi]$ are sets of uniqueness.
Externí odkaz:
http://arxiv.org/abs/1612.02849
Autor:
Veldman, Wim
The paper is a contribution to intuitionistic reverse mathematics. We work in a weak formal system for intuitionistic analysis. The Principle of Open Induction on Cantor space is the statement that every open subset of Cantor space that is progressiv
Externí odkaz:
http://arxiv.org/abs/1408.2493
Autor:
Veldman, Wim
IIn the context of a weak formal theory called Basic Intuitionistic Mathematics $\mathsf{BIM}$, we study Brouwer's Fan Theorem and a strong negation of the Fan Theorem, Kleene's Alternative (to the Fan Theorem). We prove that the Fan Theorem is equiv
Externí odkaz:
http://arxiv.org/abs/1311.6988
Autor:
Veldman, Wim
The paper is a contribution to intuitionistic reverse mathematics. We introduce a formal system called Basic Intuitionistic Mathematics BIM, and then search for statements that are, over BIM, equivalent to Brouwer's Fan Theorem or to its positive den
Externí odkaz:
http://arxiv.org/abs/1106.2738
Autor:
Veldman, Wim
We study `definable' subsets of Baire space $\mathcal{N}$. The logic of our arguments is intuitionistic and we use L.E.J.~Brouwer's Thesis on bars in $\mathcal{N}$ and his continuity axioms. We avoid the operation of taking the complement of a subset
Externí odkaz:
http://arxiv.org/abs/1104.3077
