Authors: Lopez, Fulgencio
Todorčević, Stevo 
Title: Trees and gaps from a construction scheme
Journal: Proceedings of the American Mathematical Society
Volume: 145
Issue: 2
First page: 871
Last page: 879
Issue Date: 1-Jan-2017
ISSN: 0002-9939
DOI: 10.1090/proc/13431
Abstract: 
We present simple constructions of trees and gaps using a general construction scheme that can be useful in constructing many other structures. As a result, we solve a natural problem about Hausdorff gaps in the quotient algebra P(ω)/Fin found in the literature. As it is well known, Hausdorff gaps can sometimes be filled in ω1-preserving forcing extensions. There are two natural conditions on Hausdorff gaps, dubbed S and T in the literature, that guarantee the existence of such forcing extensions. In part, these conditions are motivated by analogies between fillable Hausdorff gaps and Suslin trees. While the condition S is equivalent to the existence of ω1-preserving forcing extensions that fill the gap, we show here that its natural strengthening T is in fact strictly stronger.
Keywords: Construction schemes | Destructible gaps | S-gaps | Suslin tree | T-gaps
Publisher: American Mathematical Society

Show full item record

SCOPUSTM   
Citations

2
checked on Jan 30, 2023

Page view(s)

24
checked on Jan 31, 2023

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.