اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA model with everything except for a well-ordering of the reals
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We construct a model of $mathsf{ZF} + mathsf{DC}$ containing a Luzin set, a Sierpi{n}ski set, as well as a Burstin basis but in which there is no a well ordering of the continuum.
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N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite colouring of $mathbb R$ so that no infinite sumset $X+X={x+y:x,yin X}$ is monochromatic. Our aim in this paper is to prove a consistency result in the opposite d
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Let $M^sharp_n(mathbb{R})$ denote the minimal active iterable extender model which has $n$ Woodin cardinals and contains all reals, if it exists, in which case we denote by $M_n(mathbb{R})$ the class-sized model obtained by iterating the topmost meas
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