AUC Philosophica et Historica je víceoborový akademický časopis zaměřený na humanitní a společenskovědné obory (filozofie, psychologie, pedagogika, sociologie, obecné, české a hospodářské dějiny, pomocné vědy historické a archivnictví, etnologie).
Časopis je indexován v databázích CEEOL, DOAJ a EBSCO.
AUC PHILOSOPHICA ET HISTORICA, Vol 2022 No 1 (2022), 27–44
On lifting of embeddings between transitive models of set theory
Radek Honzík
DOI: https://doi.org/10.14712/24647055.2025.2
zveřejněno: 28. 02. 2025
Abstract
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, ∈) → (N, ∈) lifts to M[G] if there is j+ : (M[G], G, ∈) → (N[j+(G)], j+(G), ∈) 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.
klíčová slova: lifting of embeddings; compactness principles; fusion arguments
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