TY - JOUR
T1 - Mathias and silver forcing parametrized by density
AU - Laguzzi, Giorgio
AU - Mildenberger, Heike
AU - Stuber-Rousselle, Brendan
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/11
Y1 - 2023/11
N2 - We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse 2 ω to ω , while others are surprisingly gentle. We also study connections between regularity properties induced by these parametrized forcing notions and the Baire property.
AB - We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse 2 ω to ω , while others are surprisingly gentle. We also study connections between regularity properties induced by these parametrized forcing notions and the Baire property.
KW - Cardinal invariants
KW - Descriptive set theory
KW - Forcing
KW - Regularity properties of the real line
UR - http://www.scopus.com/inward/record.url?scp=85159678524&partnerID=8YFLogxK
U2 - 10.1007/s00153-023-00881-7
DO - 10.1007/s00153-023-00881-7
M3 - Article
SN - 0933-5846
VL - 62
SP - 965
EP - 990
JO - Archive for Mathematical Logic
JF - Archive for Mathematical Logic
IS - 7-8
ER -