# On the incomputability of computable dimension

## TL;DR

This paper demonstrates that for certain simple computable subsets of the Cantor space, various notions of dimension such as Hausdorff, constructive, and computable dimensions can be incomputable, highlighting fundamental limitations in their computability.

## Contribution

It introduces an iterative tree construction to show the incomputability of these dimensions in specific computable sets of the Cantor space.

## Key findings

- Hausdorff, constructive, and computable dimensions can be incomputable for simple sets
- The iterative tree construction reveals fundamental limits in dimension computability
- Highlights the gap between classical and computable dimension concepts

## Abstract

Using an iterative tree construction we show that for simple computable subsets of the Cantor space Hausdorff, constructive and computable dimensions might be incomputable.