Generalized pathways

TL;DR

This paper introduces a generalized concept of pathways in set theory, extending previous notions to facilitate new set-theoretic constructions and explore the largeness of cardinal characteristics.

Contribution

It generalizes the concept of pathways in set theory, providing a broader framework for set-theoretic constructions and the analysis of cardinal characteristics.

Findings

Introduces a new generalized pathway concept

Connects pathways to the largeness of cardinal characteristics

Enables new set-theoretic constructions

Abstract

We study a type of object, called a pathway (generalizing pathways in the sense of P. E. Cohen [Proc. Amer. Math. Soc. 74, No. 2 (1979), 318--321]), which is useful for several set-theoretic constructions and whose existence, in a sense, generalizes the notion of a cardinal characteristic being large.