Matches in SemOpenAlex for { <https://semopenalex.org/work/W2896987974> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2896987974 abstract "We prove two general results about the preservation of extendible and $C^{(n)}$-extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vopěnka's Principle and $C^{(n)}$-extendible cardinals under Jensen's iteration for forcing the GCH, previously obtained by Brooke-Taylor and Tsaprounis, res-pectively. We prove that $C^{(n)}$-extendible cardinals are preserved by forcing with standard Easton-support iterations for any possible $Delta_2$-definable behaviour of the power-set function on regular cardinals. We show that one can force proper class-many disagreements between the universe and HOD with respect to the calculation of successors of regular cardinals, while preserving $C^{(n)}$-extendible cardinals. We also show, assuming the GCH, that the class forcing iteration of Cummings-Foreman-Magidor for forcing $diamondsuit_{kappa^+}^+$ at every $kappa$ preserves $C^{(n)}$-extendible cardinals. We give an optimal result on the consistency of weak square principles and $C^{(n)}$-extendible cardinals. In the last section we prove another preservation result for $C^{(n)}$-extendible cardinals under very general (not necessarily definable or weakly homogeneous) class forcing iterations. As applications we prove the consistency of $C^{(n)}$-extendible cardinals with $rm{V}=rm{HOD}$, and also with $mathrm{GA}$ (the Ground Axiom) plus $mathrm{V}neq mathrm{HOD}$, the latter being a strengthening of a result by Hamkins, Reitz and Woodin." @default.
- W2896987974 created "2018-10-26" @default.
- W2896987974 creator A5018296270 @default.
- W2896987974 creator A5066917101 @default.
- W2896987974 date "2018-10-22" @default.
- W2896987974 modified "2023-09-28" @default.
- W2896987974 title "More on the preservation of large cardinals under class forcing" @default.
- W2896987974 cites W1727185926 @default.
- W2896987974 cites W19898668 @default.
- W2896987974 cites W2029038421 @default.
- W2896987974 cites W2035571970 @default.
- W2896987974 cites W2048739378 @default.
- W2896987974 cites W2067012191 @default.
- W2896987974 cites W2071474263 @default.
- W2896987974 cites W2130670935 @default.
- W2896987974 cites W2318231933 @default.
- W2896987974 cites W2528948859 @default.
- W2896987974 cites W2753789290 @default.
- W2896987974 cites W2897231078 @default.
- W2896987974 hasPublicationYear "2018" @default.
- W2896987974 type Work @default.
- W2896987974 sameAs 2896987974 @default.
- W2896987974 citedByCount "1" @default.
- W2896987974 countsByYear W28969879742019 @default.
- W2896987974 crossrefType "posted-content" @default.
- W2896987974 hasAuthorship W2896987974A5018296270 @default.
- W2896987974 hasAuthorship W2896987974A5066917101 @default.
- W2896987974 hasConcept C108710211 @default.
- W2896987974 hasConcept C114614502 @default.
- W2896987974 hasConcept C118615104 @default.
- W2896987974 hasConcept C134306372 @default.
- W2896987974 hasConcept C154945302 @default.
- W2896987974 hasConcept C197115733 @default.
- W2896987974 hasConcept C2524010 @default.
- W2896987974 hasConcept C2776436953 @default.
- W2896987974 hasConcept C2777212361 @default.
- W2896987974 hasConcept C33923547 @default.
- W2896987974 hasConcept C41008148 @default.
- W2896987974 hasConceptScore W2896987974C108710211 @default.
- W2896987974 hasConceptScore W2896987974C114614502 @default.
- W2896987974 hasConceptScore W2896987974C118615104 @default.
- W2896987974 hasConceptScore W2896987974C134306372 @default.
- W2896987974 hasConceptScore W2896987974C154945302 @default.
- W2896987974 hasConceptScore W2896987974C197115733 @default.
- W2896987974 hasConceptScore W2896987974C2524010 @default.
- W2896987974 hasConceptScore W2896987974C2776436953 @default.
- W2896987974 hasConceptScore W2896987974C2777212361 @default.
- W2896987974 hasConceptScore W2896987974C33923547 @default.
- W2896987974 hasConceptScore W2896987974C41008148 @default.
- W2896987974 hasLocation W28969879741 @default.
- W2896987974 hasOpenAccess W2896987974 @default.
- W2896987974 hasPrimaryLocation W28969879741 @default.
- W2896987974 hasRelatedWork W1822813779 @default.
- W2896987974 hasRelatedWork W1978359612 @default.
- W2896987974 hasRelatedWork W1992619075 @default.
- W2896987974 hasRelatedWork W1995860738 @default.
- W2896987974 hasRelatedWork W2019751722 @default.
- W2896987974 hasRelatedWork W2019819455 @default.
- W2896987974 hasRelatedWork W2052609384 @default.
- W2896987974 hasRelatedWork W2062673218 @default.
- W2896987974 hasRelatedWork W2090209200 @default.
- W2896987974 hasRelatedWork W2099202455 @default.
- W2896987974 hasRelatedWork W2106200555 @default.
- W2896987974 hasRelatedWork W2164277961 @default.
- W2896987974 hasRelatedWork W2528948859 @default.
- W2896987974 hasRelatedWork W2755408663 @default.
- W2896987974 hasRelatedWork W2897231078 @default.
- W2896987974 hasRelatedWork W2963128566 @default.
- W2896987974 hasRelatedWork W3024309854 @default.
- W2896987974 hasRelatedWork W3037992247 @default.
- W2896987974 hasRelatedWork W3041130254 @default.
- W2896987974 hasRelatedWork W3157860392 @default.
- W2896987974 isParatext "false" @default.
- W2896987974 isRetracted "false" @default.
- W2896987974 magId "2896987974" @default.
- W2896987974 workType "article" @default.