Generalized Silver and Miller measurability

TL;DR

This paper explores advanced set theory concepts related to kappa-reals, focusing on generalized notions of measurability derived from Silver and Miller trees, highlighting key similarities and differences from classical theories.

Contribution

It introduces new results on measurability notions for kappa-reals based on generalized Silver and Miller trees, expanding the understanding of their properties.

Findings

Identifies analogies with classical measurability concepts.

Highlights differences in the generalized setting.

Provides new theoretical insights into set theory of kappa-reals.

Abstract

We present some results about the burgeoning research area concerning set theory of the kappa-reals. We focus on some notions of measurability coming from generalizations of Silver and Miller trees. We present analogies and mostly differences from the classical setting.