论文信息 - A barren extension

A barren extension

It is shown that provided ω→(ω)ω, a well-known Boolean extension adds no new sets of ordinals. Under an additional assumption, the same extension preserves all strong partition cardinals. This fact elucidates the role of the hypothesis V=L[R] in the Kechris-Woodin characterization of the axiom of determinacy.

[1] J. C. Oxtoby. Measure and Category , 1971 .

[2] Everett L. Bull. Successive large cardinals , 1978 .

[3] Peter Lars Dordal. Independence results concerning some combinatorial properties of the continuum , 1982 .

[4] Eugene M. Kleinberg,et al. Infinitary combinatorics and the axiom of determinateness , 1977 .

[5] Alexander S. Kechris. The Axiom of Determinancy Implies Dependent Choices in L(R) , 1984, J. Symb. Log..

[6] Erik Ellentuck,et al. A new proof that analytic sets are Ramsey , 1974, Journal of Symbolic Logic.

[7] Arthur W. Apter. Some results on consecutive large cardinals , 1983, Ann. Pure Appl. Log..

[8] Mitchell Spector. A Measurable Cardinal with a Nonwellfounded Ultrapower , 1980, J. Symb. Log..

[9] Fred Galvin,et al. Borel sets and Ramsey's theorem , 1973, Journal of Symbolic Logic.

[10] Yiannis N. Moschovakis,et al. The axiom of determinacy, strong partition properties and nonsingular measures , 1981 .

[11] F. Hausdorff,et al. Summen von $ℵ_1$ Mengen , 1936 .

[12] G. Monro. Models of ZF with the same sets of sets of ordinals , 1973 .

[13] W H Woodin,et al. Equivalence of partition properties and determinacy. , 1983, Proceedings of the National Academy of Sciences of the United States of America.