Isomorphism types of Aronszajn trees

1985 ◽  
Vol 50 (1-2) ◽  
pp. 75-113 ◽  
Author(s):  
U. Abraham ◽  
S. Shelah
Keyword(s):  
Aronszajn Trees

Degrees of Souslin And Aronszajn Trees

1987 ◽  
Vol 33 (2) ◽  
pp. 159-170
Author(s):  
Ingrid Lindström
Keyword(s):  
Aronszajn Trees

scholarly journals Weak square sequences and special Aronszajn trees

2013 ◽  
Vol 221 (3) ◽  
pp. 267-284 ◽  
Author(s):  
John Krueger
Keyword(s):  
Aronszajn Trees ◽  
Square Sequences ◽  
Weak Square

Aronszajn trees and partitions

1985 ◽  
Vol 52 (1-2) ◽  
pp. 53-58 ◽  
Author(s):  
Stevo Todorcevic
Keyword(s):  
Aronszajn Trees

Distributive Aronszajn trees

2019 ◽  
Vol 245 (3) ◽  
pp. 217-291 ◽  
Author(s):  
Ari Meir Brodsky ◽  
Assaf Rinot
Keyword(s):  
Aronszajn Trees

Aronszajn trees and the SCH

2012 ◽  
pp. 187-206
Author(s):  
Itay Neeman ◽  
Spencer Unger
Keyword(s):  
Aronszajn Trees

scholarly journals SQUARES, ASCENT PATHS, AND CHAIN CONDITIONS

2018 ◽  
Vol 83 (04) ◽  
pp. 1512-1538 ◽  
Author(s):  
CHRIS LAMBIE-HANSON ◽  
PHILIPP LÜCKE
Keyword(s):  
Partial Order ◽  
Set Theory ◽  
Consistency Strength ◽  
Chain Conditions ◽  
Regular Cardinals ◽  
Aronszajn Tree ◽  
Square Principles ◽  
Image Position ◽  
Aronszajn Trees ◽  
Consistency Strengths

AbstractWith the help of various square principles, we obtain results concerning the consistency strength of several statements about trees containing ascent paths, special trees, and strong chain conditions. Building on a result that shows that Todorčević’s principle $\square \left( {\kappa ,\lambda } \right)$ implies an indexed version of $\square \left( {\kappa ,\lambda } \right)$, we show that for all infinite, regular cardinals $\lambda < \kappa$, the principle $\square \left( \kappa \right)$ implies the existence of a κ-Aronszajn tree containing a λ-ascent path. We then provide a complete picture of the consistency strengths of statements relating the interactions of trees with ascent paths and special trees. As a part of this analysis, we construct a model of set theory in which ${\aleph _2}$-Aronszajn trees exist and all such trees contain ${\aleph _0}$-ascent paths. Finally, we use our techniques to show that the assumption that the κ-Knaster property is countably productive and the assumption that every κ-Knaster partial order is κ-stationarily layered both imply the failure of $\square \left( \kappa \right)$.

scholarly journals Normal Spanning Trees, Aronszajn Trees and Excluded Minors

2001 ◽  
Vol 63 (1) ◽  
pp. 16-32 ◽  
Author(s):  
Reinhard Diestel ◽  
Imre Leader
Keyword(s):  
Spanning Trees ◽  
Aronszajn Trees ◽  
Excluded Minors

scholarly journals ON WIDE ARONSZAJN TREES IN THE PRESENCE OF MA

2020 ◽  
pp. 1-18
Author(s):  
MIRNA DŽAMONJA ◽  
SAHARON SHELAH
Keyword(s):  
Aronszajn Trees
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