Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Force to change large cardinal strength   This dissertation includes many theorems which show how to change large
cardinal properties with forcing. I consider in detail the degrees of
inaccessible cardinals (an analogue of the classical degrees of Mahlo
cardinals) and provide new large cardinal definitions for degrees of
inaccessible cardinals extending the hyper-inaccessible hierarchy. I showed
that for every cardinal $\kappa$, and ordinal $\alpha$, if $\kappa$ is
$\alpha$-inaccerssible, then there is a $\mathbb{P}$ forcing that $\kappa$
which preserves that $\alpha$-inaccessible but destorys that $\kappa$ is
$(\alpha+1)$-inaccessible. I also consider Mahlo cardinals and degrees of Mahlo
cardinals. I showed that for every cardinal $\kappa$, and ordinal $\alpha$,
there is a notion of forcing $\mathbb{P}$ such that $\kappa$ is still
$\alpha$-Mahlo in the extension, but $\kappa$ is no longer $(\alpha +1)$-Mahlo.
I also show that a cardinal $\kappa$ which is Mahlo in the ground model can
have every possible inaccessible degree in the forcing extension, but no longer
be Mahlo there. The thesis includes a collection of results which give forcing
notions which change large cardinal strength from weakly compact to weakly
measurable, including some earlier work by others that fit this theme. I
consider in detail measurable cardinals and Mitchell rank. I show how to change
a class of measurable cardinals by forcing to an extension where all measurable
cardinals above some fixed ordinal $\alpha$ have Mitchell rank below $\alpha.$
Finally, I consider supercompact cardinals, and a few theorems about strongly
compact cardinals. Here, I show how to change the Mitchell rank for
supercompactness for a class of cardinals.

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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: cs