Set-theoretic blockchains

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F19%3A00348720" target="_blank" >RIV/68407700:21240/19:00348720 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11210/19:10383651 RIV/00216208:11320/19:10383651

Výsledek na webu

<a href="https://doi.org/10.1007/s00153-019-00672-z" target="_blank" >https://doi.org/10.1007/s00153-019-00672-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00153-019-00672-z" target="_blank" >10.1007/s00153-019-00672-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Set-theoretic blockchains

Popis výsledku v původním jazyce

Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize these embeddings via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs.

Název v anglickém jazyce

Set-theoretic blockchains

Popis výsledku anglicky

Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize these embeddings via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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

1432-0665

Svazek periodika

58

Číslo periodika v rámci svazku

7-8

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

33

Strana od-do

965-997

Kód UT WoS článku

000485978400011

EID výsledku v databázi Scopus

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