Inequality in constructive mathematics.

Constructive Mathematics

Constructive Mathematics , in

The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop’s constructive mathematics (BISH). It gives a sketch of both Myhill’s axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin...

Constructive mathematics without choice

What becomes of constructive constructive mathematics without the axiom of (countable) choice? Using illustrations from a variety of areas, it is argued that it becomes better. Despite the apparent unanimity among schools of constructive mathematics with respect to the acceptance of the countable axiom of choice, I believe it to be one of the central problems, or mysteries, of constructive math...

Informal Constructive Reverse Mathematics

Constructive Mathematics and Quantum Physics †

Our discussion takes place in the context of Bishop’s constructive mathematics (BISH; [3, 4]), in which “existence” is interpreted strictly as “constructibility.”3 One distinctive feature of BISH, compared with other varieties of constructive mathematics is that its results and proofs can be interpreted mutatis mutandis within classical (that is, traditional) mathematics, recursive mathematics ...