Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T17:19:55.000Z Has data issue: false hasContentIssue false

Chapter 11 - A proof of square in LSA-small HOD mice

Published online by Cambridge University Press:  07 June 2024

Grigor Sargsyan  and
Nam Trang
Grigor Sargsyan
Affiliation:
Polish Academy of Sciences
Nam Trang
Affiliation:
University of North Texas
Get access

Summary

This chapter presents a proof $\square_{\kappa,2}$ holds in a lsa-small hod mouse $\mathcal{P}$ for all cardinals $\kappa$ of $\mathcal{P}$. The proof adapts a well-known construction of $\square$ in extender models by Schimmerling-Zeman. The main challenge to overcome in this situation is that the full condensation lemma, which holds for extender models, does not hold in hod mice. The main application of this result is in the proof of consistency of LSA in Chapter 12.

Keywords

Squarelsa-small hod mouselocally strong branch condensationlocally strongly fullness preserving
Type
Chapter
Information
The Largest Suslin Axiom , pp. 309 - 334
Publisher: Cambridge University Press
Print publication year: 2024

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×