11 citations · 18 across the 6 of their papers we have counts for
7 papers
Maximal ideals in countable rings, constructively
Ingo Blechschmidt, Peter Schuster
The existence of a maximal ideal in a general nontrivial commutative ring is tied together with the axiom of choice. Following Berardi, Valentini and thus Krivine but using the rel…
Exploring mathematical objects from custom-tailored mathematical universes
Ingo Blechschmidt
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathemat…
Using the internal language of toposes in algebraic geometry
Ingo Blechschmidt
Any scheme has its associated little and big Zariski toposes. These toposes support an internal mathematical language which closely resembles the usual formal language of mathemati…
Generalized spaces for constructive algebra
Ingo Blechschmidt
The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algeb…
A constructive Knaster-Tarski proof of the uncountability of the reals
Ingo Blechschmidt, Matthias Hutzler
We give an uncountability proof of the reals which relies on their order completeness instead of their sequential completeness. We use neither a form of the axiom of choice nor the…
Flabby and injective objects in toposes
Ingo Blechschmidt
We introduce a general notion of flabby objects in elementary toposes and study their basic properties. In the special case of localic toposes, this notion reduces to the common no…