We use a variation on Mason's alpha-function as a pre-dimension function to construct a not one-based omega-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 omega.
A NEW omega-STABLE PLANE
Paolini, G
2020-01-01
Abstract
We use a variation on Mason's alpha-function as a pre-dimension function to construct a not one-based omega-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 omega.
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