Cardinal sequences of LCS spaces under GCH

TL;DR

This paper characterizes which sequences of regular cardinals can be realized as the cardinal sequences of locally compact scattered spaces assuming GCH, using constructions of universal spaces.

Contribution

It provides a complete characterization of possible cardinal sequences under GCH, advancing understanding of LCS spaces.

Findings

Full characterization of cardinal sequences under GCH

Construction of universal locally compact scattered spaces

Clarification of possible sequences in LCS spaces

Abstract

We give full characterization of the sequences of regular cardinals that may arise as cardinal sequences of locally compact scattered spaces under GCH. The proofs are based on constructions of universal locally compact scattered spaces.