On lifting of embeddings between transitive models of set theory
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F25%3A10510624" target="_blank" >RIV/00216208:11210/25:10510624 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Z1chUVyTU7" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Z1chUVyTU7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/24647055.2025.2" target="_blank" >10.14712/24647055.2025.2</a>
Alternative languages
Result language
angličtina
Original language name
On lifting of embeddings between transitive models of set theory
Original language description
Suppose M and N are transitive models of set theory, P is a forcing notion in M and G is P-generic over M. An elementary embedding j : (M, ELEMENT OF) RIGHTWARDS ARROW (N, ELEMENT OF) lifts to M[G] if there is j+ : (M[G], G, ELEMENT OF) RIGHTWARDS ARROW (N[j+(G)], j+(G), ELEMENT OF) such that j+ restricted to M is equal to j. We survey some basic applications of the lifting method for both large cardinals and small cardinals (such as ω2, or successor cardinals in general). We focus on results and techniques which appeared after Cummings's handbook article [Cum10]: we for instance discuss a generalization of the surgery argument, liftings based on fusion, and compactness principles such as the tree property and stationary reflection at successor cardinals.
Czech name
—
Czech description
—
Classification
Type
J<sub>ost</sub> - Miscellaneous article in a specialist periodical
CEP classification
—
OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology
Result continuities
Project
<a href="/en/project/GA24-12141S" target="_blank" >GA24-12141S: The role of set theory in modern mathematics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Acta Universitatis Carolinae. Philosophica et Historica
ISSN
0567-8293
e-ISSN
2464-7055
Volume of the periodical
2022
Issue of the periodical within the volume
1
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
19
Pages from-to
27-45
UT code for WoS article
—
EID of the result in the Scopus database
—