Splitting Localization and Prediction Numbers

TL;DR

This paper revisits previous work on evasion and prediction numbers, introduces a new variation of the localization property, and employs a specialized forcing notion with accelerating trees to address related questions.

Contribution

It defines the $(k+1)^{ ext{omega}}$-localization property and applies a novel forcing with accelerating trees to explore localization and prediction numbers.

Findings

Introduces the $(k+1)^{ ext{omega}}$-localization property.

Develops a forcing notion with accelerating trees.

Provides insights into evasion and prediction numbers.

Abstract

In this paper the work done by Newelski and Roslanowski is revisited to solve a question done by Blass about one of the possible evasion and prediction numbers. This led to define a variation of the $k$-localization property (the $(k+1)^{\omega}$-localization property) and the use of a forcing notion with accelerating trees.