# nLab Russian constructivism

Russian constructivism

# Russian constructivism

## Summary

The Russian school of constructive mathematics, associated principally with Andrey Markov Jr, was (is?) a variety of constructive mathematics focussing on recursion theory.

## Principles and results

• Classically true principles (not always accepted by other constructivists):
• Classically false principles:
• every partial function from $\mathbb{N}$ to $\mathbb{N}$ is computable;
• every set is a subquotient of $\mathbb{N}$.
• Classically false results (false w.r.t. classical functions and sets):
• every total function from $\mathbb{R}$ (the real line) to $\mathbb{R}$ is pointwise continuous (Ceitin's theorem?);
• there exist continuous functions from $[0,1]$ (the unit interval) to $\mathbb{R}$ that are pointwise continuous but not uniformly continuous;
• there exist bounded sets of real numbers with no supremum (given by Specker sequences).

Last revised on February 19, 2020 at 11:05:01. See the history of this page for a list of all contributions to it.