Forcing square with small conditions

We show that if $κ^{<κ} = κ$, then there is a $κ$-strategically closed, $κ^+$-c.c.\ partial order that forces $\square_κ$. We discuss consequences for generic large cardinals.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.34900
Primary Topic
Advanced Topology and Set Theory
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Forcing square with small conditions

Monroe Eskew
arXiv (Cornell University)
Advanced Topology and Set Theory
preprint

Forcing square with small conditions

Monroe Eskew
preprint en

Abstract

We show that if $κ^{<κ} = κ$, then there is a $κ$-strategically closed, $κ^+$-c.c.\ partial order that forces $\square_κ$. We discuss consequences for generic large cardinals.

arXiv (Cornell University)
Advanced Topology and Set Theory
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon
Forcing square with small conditions — Monroe Eskew · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS