TY - JOUR
T1 - Fresh Function Spectra
AU - Fischer, Vera
AU - Koelbing, Marlene Elisabeth
AU - Wohofsky, Wolfgang
PY - 2023/10
Y1 - 2023/10
N2 - In this paper, we investigate the fresh function spectrum of forcing notions, where a new function on an ordinal is called fresh if all its initial segments are in the ground model. We determine the fresh function spectrum of several forcing notions and discuss the difference between fresh functions and fresh subsets. Furthermore, we consider the question which sets are realizable as the fresh function spectrum of a homogeneous forcing. We show that under GCH all sets with a certain closure property are realizable, while consistently there are sets which are not realizable.
AB - In this paper, we investigate the fresh function spectrum of forcing notions, where a new function on an ordinal is called fresh if all its initial segments are in the ground model. We determine the fresh function spectrum of several forcing notions and discuss the difference between fresh functions and fresh subsets. Furthermore, we consider the question which sets are realizable as the fresh function spectrum of a homogeneous forcing. We show that under GCH all sets with a certain closure property are realizable, while consistently there are sets which are not realizable.
KW - Chain conditions
KW - Easton product
KW - Fresh subset
KW - Refining matrices
KW - Todorčević's maximality principle
KW - Tree forcings
UR - http://www.scopus.com/inward/record.url?scp=85162742281&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2023.103300
DO - 10.1016/j.apal.2023.103300
M3 - Article
SN - 0168-0072
VL - 174
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 9
M1 - 103300
ER -