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4 papers
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…
An elementary and constructive proof of Grothendieck's generic freeness lemma
Ingo Blechschmidt
We present a new and direct proof of Grothendieck's generic freeness lemma in its general form. Unlike the previously published proofs, it does not proceed in a series of reduction…