A strong partition cardinal above $$\varTheta $$ |
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Authors: | Daniel W Cunningham |
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Institution: | 1.Mathematics Department,SUNY Buffalo State,Buffalo,USA |
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Abstract: | Assuming \(\text {ZF}+\text {DC}\), we prove that if there exists a strong partition cardinal greater than \(\varTheta \), then (1) there is an inner model of \(\text {ZF}+\text {AD}+\text {DC}+ {{{\mathbb {R}}} }^{{\#}}\) exists, and (2) there is an inner model of \(\text {ZF}+\text {AD}+\text {DC}+ (\exists \kappa >\varTheta )\,(\kappa \) is measurable). Here \(\varTheta \) is the supremum of the ordinals which are the surjective image of the set of reals \({{{\mathbb {R}}} }\). |
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