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D. W. Cunningham

Publications and source records attributed to D. W. Cunningham.

3 recordsLinked to original sources
arXiv2006

Scales and the fine structure of K(R). Part I: Acceptability above the reals

This article is Part I in a series of three papers devoted to determining the minimal complexity of scales in the inner model $K(\mathbb{R})$. Here, in Part I, we shall complete our development of a fine structure theory for $K(\mathbb{R})$ which is essential for our work in Parts II and III. In particular, we prove the following fundamental theorem which supports our analysis of scales in $K(\mathbb{R})$: If $\mathcal{M}$ is an iterable real premouse, then $\mathcal{M}$ is acceptable above the reals. This theorem will be used in Parts II and III to solve the problem of finding scales of minimal complexity in $K(\mathbb{R})$.

math.LO↗
arXiv2006

Scales and the fine structure of K(R). Part II: Weak real mice and scales

We define weak real mice $\mathcal{M}$ and prove that the boldface pointclass $\boldsymbolΣ_m(\mathcal{M})$ has the scale property assuming only the determinacy of sets of reals in $\mathcal{M}$ when $m$ is the smallest integer $m>0$ such that $\boldsymbolΣ_m(\mathcal{M})$ contains a set of reals not in $\mathcal{M}$. We shall use this development in Part III to obtain scales of minimal complexity in $K(\mathbb{R})$.

math.LO↗