Measures in Mice

Farmer Schlutzenberg

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arXiv · 1301.4702

Measures in Mice

Farmer Schlutzenberg

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Abstract

This thesis analyses extenders in fine structural mice. Kunen showed that in the inner model for one measurable cardinal, there is a unique measure. This result is generalized, in various ways, to mice below a superstrong cardinal. The analysis is then used to show that certain tame mice satisfy $V=\mathsf{HOD}$. In particular, the approach proides a new proof of this result for the inner model $M_n$ for $n$ Woodin cardinals. It is also shown that in $M_n$, all homogeneously Suslin sets of reals are $\mathbfΔ^1_{n+1}$.

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BibTeX RIS

Farmer Schlutzenberg. 2013-01-20. Measures in Mice. https://arxiv.org/abs/1301.4702

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