论文信息 - ω1 can be measurable

ω1 can be measurable

It is shown that ifZF + the axiom of choice + “there is a measurable cardinal” is consistent thenZF + “ω1 is measurable” is consistent. The corresponding model is a symmetric submodel of the Cohen-type extension which collapses the first measurable cardinal onto ω0.

T. Jech

[1] A. Levy,et al. Measurable cardinals and the continuum hypothesis , 1967 .

[2] Alfred Tarski,et al. From accessible to inaccessible cardinals (Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones) , 1964 .

[3] Petr Vopěnka. General theory of $\nabla$-models , 1967 .