First counterexamples are given to a basic question raised in: M. Marshall, Open questions in the theory of spaces of orderings, J. Symbolic Logic 67 (2002), 341352. The paper considers the space of orderings (X,G) of the function field of a real irreducible conic C over the field Q of rational numbers. It is shown that the pp conjecture fails to hold for such a space of orderings when C has no...