Potential isomorphism and semi-proper trees

Alex Hellsten, Tapani Hyttinen, and Saharon Shelah. "Potential isomorphism and semi-proper trees." Fundamenta Mathematicae 175.2 (2002): 127-142. <http://eudml.org/doc/283136>.

@article{AlexHellsten2002,
abstract = { We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the cardinality of the models. We introduce the notion of weakly semi-proper trees, and note that there is a strong connection between the existence of potentially isomorphic models for a given complete theory and the existence of weakly semi-proper trees. We show that the existence of weakly semi-proper trees is consistent relative to ZFC by proving the existence of weakly semi-proper trees under certain cardinal arithmetic assumptions. We also prove the consistency of the non-existence of weakly semi-proper trees assuming the consistency of some large cardinals. },
author = {Alex Hellsten, Tapani Hyttinen, Saharon Shelah},
journal = {Fundamenta Mathematicae},
keywords = {potential isomorphism; weakly semi-proper trees; cardinal arithmetic; consistency; large cardinals},
language = {eng},
number = {2},
pages = {127-142},
title = {Potential isomorphism and semi-proper trees},
url = {http://eudml.org/doc/283136},
volume = {175},
year = {2002},
}

TY - JOUR
AU - Alex Hellsten
AU - Tapani Hyttinen
AU - Saharon Shelah
TI - Potential isomorphism and semi-proper trees
JO - Fundamenta Mathematicae
PY - 2002
VL - 175
IS - 2
SP - 127
EP - 142
AB - We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the cardinality of the models. We introduce the notion of weakly semi-proper trees, and note that there is a strong connection between the existence of potentially isomorphic models for a given complete theory and the existence of weakly semi-proper trees. We show that the existence of weakly semi-proper trees is consistent relative to ZFC by proving the existence of weakly semi-proper trees under certain cardinal arithmetic assumptions. We also prove the consistency of the non-existence of weakly semi-proper trees assuming the consistency of some large cardinals.
LA - eng
KW - potential isomorphism; weakly semi-proper trees; cardinal arithmetic; consistency; large cardinals
UR - http://eudml.org/doc/283136
ER -