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A new ω-stable plane

Paolini Gianluca

Reports on Mathematical Logic

2020

Vol. 55

87--111

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 T h(P), we prove that algebraic closure and intrinsic closure coincide in T h(P), and we show that T h(P) fails weak elimination of imaginaries, and has Morley rank ω.