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:

1. He seems not to assume the existence of an inaccessible cardinal in the ground model, is this correct?

2. 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?

3. 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://www.academie-sciences.fr/activite/archive/ressource.htm

In a paper by J.-L. Krivine, Modèles de ZF+AC dans lesquels tout ensemble de réels définissable en termes d'ordinaux est mesurable-Lebesgue [C. R. Acad. Sci. Paris Sér. A-B 269 (1969), A549–A552, MR0253894], he presents a model of ZFC in which every set of reals definable from ordinals is Lebesgue measurable.

My question is:

1. He seems not to assume the existence of an inaccessible cardinal in the ground model, is this correct?

2. 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?

3. Does Theorem 3 of that paper still hold if we replace "Lebesgue measurable" by "having the property of Baire"?

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:

1. He seems not to assume the existence of an inaccessible cardinal in the ground model, is this correct?

2. 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?

3. 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

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:

1. He seems not to assume the existence of an inaccessible cardinal in the ground model, is this correct?

2. 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?

3. 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://www.academie-sciences.fr/activite/archive/ressource.htm