Chain conditions in maximal models

Paul Larson, and Stevo Todorčević. "Chain conditions in maximal models." Fundamenta Mathematicae 168.1 (2001): 77-104. <http://eudml.org/doc/281722>.

@article{PaulLarson2001,
abstract = {We present two $ℙ_\{max\}$ varations which create maximal models relative to certain counterexamples to Martin’s Axiom, in hope of separating certain classical statements which fall between MA and Suslin’s Hypothesis. One of these models is taken from [19], in which we maximize relative to the existence of a certain type of Suslin tree, and then force with that tree. In the resulting model, all Aronszajn trees are special and Knaster’s forcing axiom ₃ fails. Of particular interest is the still open question whether ₂ holds in this model.},
author = {Paul Larson, Stevo Todorčević},
journal = {Fundamenta Mathematicae},
keywords = {maximal models; Martin's axiom; Suslin's hypothesis; Suslin tree; Aronszajn trees; forcing},
language = {eng},
number = {1},
pages = {77-104},
title = {Chain conditions in maximal models},
url = {http://eudml.org/doc/281722},
volume = {168},
year = {2001},
}

TY - JOUR
AU - Paul Larson
AU - Stevo Todorčević
TI - Chain conditions in maximal models
JO - Fundamenta Mathematicae
PY - 2001
VL - 168
IS - 1
SP - 77
EP - 104
AB - We present two $ℙ_{max}$ varations which create maximal models relative to certain counterexamples to Martin’s Axiom, in hope of separating certain classical statements which fall between MA and Suslin’s Hypothesis. One of these models is taken from [19], in which we maximize relative to the existence of a certain type of Suslin tree, and then force with that tree. In the resulting model, all Aronszajn trees are special and Knaster’s forcing axiom ₃ fails. Of particular interest is the still open question whether ₂ holds in this model.
LA - eng
KW - maximal models; Martin's axiom; Suslin's hypothesis; Suslin tree; Aronszajn trees; forcing
UR - http://eudml.org/doc/281722
ER -