Constant prediction and evasion number, I: Generalization and variants

TL;DR

This paper introduces and analyzes new cardinal invariants called the constant evasion and prediction numbers, exploring their properties, limits, and consistency results within set theory.

Contribution

It defines the constant evasion and prediction numbers, establishes their fundamental properties, and investigates their relationships and consistency results.

Findings

Defined the constant evasion and prediction numbers.

Established limits and relationships among these invariants.

Proved several consistency results related to these invariants.

Abstract

Using the concept of constant evasion to different sorts of suitable binary relations, we establish many cardinal invariants derived from the established cardinal invariants $\mathfrak{e}^\mathrm{const}_{n}$ and $\mathfrak{v}^\mathrm{const}_{n}$, called the constant evasion number and the constant prediction number. We formulate several limits and consistency results pertaining to them.