3 citations · 4 across the 3 of their papers we have counts for
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On Farkas' Lemma and Related Propositions in BISH
Josef Berger, Gregor Svindland
In this paper we analyse in the framework of constructive mathematics (BISH) the validity of Farkas' lemma and related propositions, namely the Fredholm alternative for solvability…
Brouwer's fan theorem
Josef Berger
Brouwer's fan theorem states that every bar is a uniform bar. We give an overview of the status of this axiom in Bishop's constructive mathematics. In particular, we describe the r…
A bound for Dickson's lemma
Josef Berger, Helmut Schwichtenberg
We consider a special case of Dickson's lemma: for any two functions on the natural numbers there are two numbers such that both and weakly increase on them, i.…
Constructive aspects of Riemann's permutation theorem for series
J. Berger, D. Bridges, H. Diener +1
The notions of permutable and weak-permutable convergence of a series of real numbers are introduced. Classically, these two notions are equivalent, and,…