A Laver-like indestructibility for hypermeasurable cardinals

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A Laver-like indestructibility for hypermeasurable cardinals

Popis výsledku v původním jazyce

We show that if $kappa$ is $H(mu)$-hypermeasurable for some cardinal $mu$ with $kappa &lt; cf{mu} le mu$ 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 The construction of $V^*$ is based on the ideas of Woodin (unpublished) and Cummings for preservation of measurability, but suitably generalised and simplified to achieve a more general result.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).

Název v anglickém jazyce

A Laver-like indestructibility for hypermeasurable cardinals

Popis výsledku anglicky

We show that if $kappa$ is $H(mu)$-hypermeasurable for some cardinal $mu$ with $kappa &lt; cf{mu} le mu$ 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 The construction of $V^*$ is based on the ideas of Woodin (unpublished) and Cummings for preservation of measurability, but suitably generalised and simplified to achieve a more general result.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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF15-34700L" target="_blank" >GF15-34700L: Kontinuum, forcing a velké kardinály</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Archive for Mathematical Logic

ISSN

0933-5846

e-ISSN

—

Svazek periodika

58

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

13

Strana od-do

275-287

Kód UT WoS článku

000463871300002

EID výsledku v databázi Scopus

2-s2.0-85049143911