LIST D: EIGHT PAPERS ON STRONG AXIOMS OF INFINITY
[D1] On sequences generic in the sense of Prikry,
Journal of the Australian Mathematical Society , 15
(1973) 409-414; MR 48 # 10809
(Gives a criterion that is in daily use.)
[D2] Solution of a problem of B. Rotman,
Colloquium Mathematicum, 38 (1977) p 39; MR 57 # 129
(The problem was also solved by E. Grzegorek.)
[D3] 0# and the p-point problem,
Higher Set Theory, edited by G. Mueller and D. Scott, Springer
Lecture Notes in Mathematics, 669, 375-384; MR 80f:03062
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(Uses Jensen's covering lemma to construct a non-feeble p-filter)
[D4] (with J. M. Henle) Supercontinuity, Mathematical
Proceedings of the Cambridge Philosophical Society, 92 (1982) 1-15;
MR 84h:03112
(Studies properties of strong partition cardinals, which abound when the axiom of determinacy is assumed.)
[D5] (with W. Just, K. Prikry and P. Simon)
On the existence of large p-ideals
Journal of Symbolic Logic, 55 (1990) 457-465;
MR 91g:03094
(Extension of the methods and results of [D3].)
[D6]
Strong Statements of Analysis
(Discusses examples of natural statements concerning irrational numbers
that are equivalent, provably in ZFC, to strong set-theoretical hypotheses.
12 pp of A4 plain TeX. Published
by the Bulletin of the London Mathematical Society 32
(2000) 531--526,
with a comment by Mac Lane on page 527, but in a version that contains
over 100 alterations made by the Editor of that organ in defiance
of the author's wishes. The present piece is the authentic text.)
.ps.dvi
[D7] (with Joan Bagaria and Carles Casacuberta)
Epireflections and supercompact cardinals
Journal of Pure and Applied Algebra 213 (2009) 1208-1215.
.ps
(Casacuberta and others have used Vopěnka's principle to prove that certain
functors admit representations by local functions. We weaken the set-theoretical hypothesis required, in the case that the functors satisfy stricter conditions than before.)
[D8](with Joan Bagaria, Carles Casacuberta and Jiří Rosický)
Definable orthogonality classes in accessible categories are small
J. European Math. Soc. 17 (2015) 549--589
(extends the main results of "Epireflections and supercompact cardinals" from absolute epireflective subcategories to definable reflective subcategories,
by showing that the existence of a proper class of supercompact cardinals implies that
each object in a Sigma_2-definable class of objects of an accessible category has a small subobject in the same class. That in turn shows that each Sigma_2-definable
class of objects is bounded, and thence that each absolute orthogonality class is a small-orthogonality class.
Hence, each reflection in an accessible category whose class of local objects is absolute is an F-localisation for some set F of morphisms.)
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