proceedings of the AMS Summer Research Conference on Axiomatic Set Theory, held in Boulder, Colorado, June 19--25, 1983. This was the first large meeting devoted exclusively to set theory since the legendary 1967 UCLA meeting, and a large majority of the most active research mathematicians in the field participated. All areas of set theory, including constructibility, forcing, combinatorics and descriptive set theory, were represented; many of the papers in the proceedings explore connections between areas. Readers should have a background of graduate-level set theory. There is a paper by S.~Shelah applying proper forcing to obtain consistency results on combinatorial cardinal "invariants" below the continuum, and papers by R.~David and S.~Freidman on properties of $0^#$. Papers by A.~Blass, H.-D.~Donder, T.~Jech and W.~Mitchell involve inner models with measurable cardinals and various combinatorial properties. T.~Carlson largely solves the pin-up problem, and D.~Velleman presents a novel construction of a Souslin tree from a morass. S.~Todorcevic obtains the strong failure of the qedprinciple from the Proper Forcing Axiom and A.~Miller discusses properties of a new species of perfect-set forcing. H.~Becker and A.~Kechris attack the third Victoria Delfino problem while W.~Zwicker looks at combinatorics on $P_kappa(lambda)$ and J.~Henle studies infinite-exponent partition relations. A.~Blass shows that if every vector space has a basis then $AC$ holds. I.~Anellis treats the history of set theory, and W.~Fleissner presents set-theoretical axioms of use in general topology.

Hide more