A New w-Stable Plane Cover Image

A New w-Stable Plane
A New w-Stable Plane

Author(s): Gianluca Paolini
Subject(s): Logic, Analytic Philosophy, Methodology and research technology
Published by: Wydawnictwo Uniwersytetu Jagiellońskiego
Keywords: Hrushovski constructions; matroids; w-stable structures;

Summary/Abstract: We use a variation on Mason’s α-function as a pre-dimension function to construct a not one-based w-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 w.

  • Issue Year: 2020
  • Issue No: 55
  • Page Range: 87-111
  • Page Count: 25
  • Language: English