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TREES AND STATIONARY REFLECTION AT DOUBLE SUCCESSORS OF REGULAR CARDINALS
Published online by Cambridge University Press: 14 February 2022
Abstract
We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals
$\kappa $
, updating some classical constructions in the process. This includes models of
$\mathsf {CSR}(\kappa ^{++})\wedge {\sf TP}(\kappa ^{++})$
(both with and without
${\sf AP}(\kappa ^{++})$
) and models of the conjunctions
${\sf SR}(\kappa ^{++}) \wedge \mathsf {wTP}(\kappa ^{++}) \wedge {\sf AP}(\kappa ^{++})$
and
$\neg {\sf AP}(\kappa ^{++}) \wedge {\sf SR}(\kappa ^{++})$
(the latter was originally obtained in joint work by Krueger and the first author [9], and is here given using different methods). Analogs of these results with the failure of
$\sf {SH}(\kappa ^{++})$
are given as well. Finally, we obtain all of our results with an arbitrarily large
$2^\kappa $
, applying recent joint work by Honzik and the third author.
Keywords
MSC classification
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
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