In a paper by J. L. Krivine which appeared in "Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. Séries A et B 269: A549––A552", ISSN 0151-0509, MR 0253894, he presents a model of ZFC in which every set of reals definable from ordinals is Lebesgue measurable.
My question is:
He seems not to assume the existence of an inaccessible cardinal in the ground model, is this correct?
In Theorem 3 of that paper, he concludes that every set of reals definable from ordinals is Lebesgue measurable. Does this continue to hold if we replace definable from ordinals by definable from a countable sequence of ordinals?
Does Theorem 3 of that paper still hold if we replace "Lebesgue measurable" by "having the property of Baire"?
PS: This paper is referred to in the Wikipedia article about the Solovay's model. It is available on http://gallica.bnf.fr/ark:/12148/bpt6k4802973