# Computable analogs of cardinal characteristics: Prediction and Rearrangement

## TL;DR

This paper explores computable analogs of cardinal characteristics of the continuum, translating properties like the evasion and prediction numbers into highness notions in Turing degrees, and maps them within a computability-theoretic framework.

## Contribution

It introduces four new highness notions derived from cardinal invariants and situates them in the computability-theoretic version of Cichoń's diagram.

## Key findings

- Defined four new highness notions from cardinal invariants.
- Established basic properties of these highness notions.
- Mapped these notions within the computability-theoretic Cichoń's diagram.

## Abstract

There has recently been work by multiple groups in extracting the properties associated with cardinal invariants of the continuum and translating these properties into similar analogous combinatorial properties of computational oracles. Each property yields a highness notion in the Turing degrees. In this paper we study the highness notions that result from the translation of the evasion number and its dual, the prediction number, as well as two versions of the rearrangement number. When translated appropriately, these yield four new highness notions. We will define these new notions, show some of their basic properties and place them in the computability-theoretic version of Cicho\'{n}'s diagram.