TY - JOUR
TI - A New w-Stable Plane
AU - Paolini, Gianluca
TI - A New w-Stable Plane
AB - We use a variation on Mason’s α-function as a pre-dimension function to construct a not one-based ω–stable plane P (i.e. a simple rank 3 matroid) which does not admit an algebraic representation (in the sense of matroid theory) over any field. Furthermore, we characterize forking in Th(P), we prove that algebraic closure and intrinsic closure coincide in Th(P), and we show that Th(P) fails weak elimination of imaginaries, and has Morley rank ω.
VL - 2020
IS - Number 55
PY - 2020
SN - 0137-2904
C1 - 2084-2589
SP - 87
EP - 111
DO - 10.4467/20842589RM.20.005.12437
UR - https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/a-new-w-stable-plane
KW - Hrushovski constructions
KW - matroids
KW - w-stable structures