LIST A: PAPERS ON INFINITARY RAMSEY THEORY, and my dissertation of 1968

[A1] Happy families, Annals of Mathematical Logic 12 (1977) 59--111; MR 58 \# 10462

[A2] A remark on rare filters, Colloquium Mathematicae Societatis Janos Bolyai Volume 10, (North Holland, 1974), 1095-1097; MR 51 # 10098

[A3] (with J. M. Henle and H. Woodin) A barren extension, Proceedings of the VIth Latin American Logic Colloquium, Caracas, 1983, edited by Carlos Di Prisco, Springer Lecture Notes in Mathematics, 1130, 195-207; MR 87d:03141

FROM MY ARCHIVES
On a generalisation of Ramsey's theorem Introduction 1. 2. 3. 4. 5. 6. 7. 8. 9. (Introduction: what are now called non-Ramsey sets were then called Scott families. At the time I wrote the thesis, I knew of Prikry's result that all Borel sets are Ramsey, but not that Galvin had also proved it. ¶¶ 1, 2, and 7 are largely devoted to expounding, in the language of Boolean-valued models, Solovay's construction of his celebrated model, his own account not at the time being available. ¶¶ 3, 4, 5, 6, 8 and 9 are original to me, except where stated. The key concept of a condition capturing a dense set is introduced in ¶ 4, on page 66, and applied in pages 72-77 to prove the ``all subsets generic" property for "plain Mathias" forcing, and later, on page 80, to establish the Prikry property for this forcing. ¶¶ 5 and 6 digress from the main proof; ¶ 5 explores properties of Mathias reals, and has recently borne fruit by showing, answering a question of Zapletal, that if R is an analytic equivalence relation on the power set of omega in which every equivalence class is countable, then, ``almost everywhere", xRy implies that the symmetric difference of x and y is finite. ¶ 6 compares Mathias reals with other kinds of generic real known at the time. ¶ 7 analyses collapsing algebras; in ¶ 8 it is shown that in Lévy's model obtained by collapsing an inaccessible all definable families are Ramsey, and then in ¶ 9 MacAloon's method is followed to obtain "all sets Ramsey" in an appropriate submodel.

Back to the top of publications

Back to the homepage