The extent of saturation of induced ideals

TL;DR

This paper constructs a model featuring a saturated ideal over a power set and investigates how extensively such an ideal can be saturated.

Contribution

It introduces a new model with a saturated ideal and analyzes the limits of its saturation properties.

Findings

Constructed a model with a saturated ideal over _{} .

Studied the extent and limitations of saturation of the ideal.

Provided insights into the structure of saturated ideals in set theory.

Abstract

We construct a model with a saturated ideal $I$ over $\mathcal{P}_{\kappa}\lambda$ and study the extent of saturation of $I$.