A Laver-like indestructibility for hypermeasurable cardinals

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F19%3A10385821" target="_blank" >RIV/00216208:11210/19:10385821 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=4SLMKwE88w" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=4SLMKwE88w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00153-018-0637-0" target="_blank" >10.1007/s00153-018-0637-0</a>

Result language
angličtina
Original language name
A Laver-like indestructibility for hypermeasurable cardinals
Original language description
We show that if $kappa$ is $H(mu)$-hypermeasurable for some cardinal $mu$ with $kappa < cf{mu} le mu$ and GCH holds, then we can extend the universe by a cofinality-preserving forcing to obtain a model $V^*$ in which the $H(mu)$-hyper-measurability of $kappa$ is indestructible by the Cohen forcing at $kappa$ of any length up to $mu$ (in particular $kappa$ is $H(mu)$-hypermeasurable in $V^*$). The preservation of hypermeasurability (in contrast to preservation of mere measurability) is useful for subsequent arguments (such as the definition of Radin forcing). The construction of $V^*$ is based on the ideas of Woodin (unpublished) and Cummings for preservation of measurability, but suitably generalised and simplified to achieve a more general result. Unlike the Laver preparation for a supercompact cardinal, our preparation non-trivially increases the value of $2^{kappa^+}$, which is greater or equal to $mu$ in $V^*$ (but $2^kappa =kappa^+$ is still true in $V^*$ if we start with GCH).
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF15-34700L" target="_blank" >GF15-34700L: The continuum, forcing and large cardinals</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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