Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313447768> ?p ?o ?g. }
Showing items 1 to 39 of
39
with 100 items per page.
- W4313447768 abstract "For $n<omega$, let $N_n$ be the minimal iterable proper class mouse $M$ such that $Mmodels$ there are ordinals $delta_0<kappa_0<ldots<delta_{n-1}<kappa_{n-1}$ such that each $delta_i$ is a Woodin cardinal and each $kappa_i$ is a strong cardinal, and let $N_omega$ be likewise, but with $Mmodels$ there is an ordinal $lambda$ which is a limit of Woodin cardinals and a limit of strong cardinals. Under appropriate large cardinal hypotheses, Sargsyan and Schindler introduced and analysed in Varsovian models I the Varsovian model of $N_1$, and Sargsyan, Schindler and the author introduced and analysed in Varsovian models II the Varsovian model of $N_2$. We extend this to $N_omega$, assuming that $*$-translation integrates routinely with the P-constructions of this paper (the write-up of which is yet to be completed). We show, under this assumption, that $N_omega$ has a proper class inner model $mathscr{V}_omega$ which is a fully iterable strategy mouse with $omega$ Woodin cardinals, closed under its strategy, and that the universe of $mathscr{V}_omega$ is the eventual generic HOD, and the mantle, of $N_omega$. We also show, under the same assumption, that the core model $K$ of $N_omega$ (which can be defined in a natural manner) is an iterate of $N_omega$, is an inner model of $mathscr{V}_omega$, and is fully iterable in $M$ and in $mathscr{V}_omega$." @default.
- W4313447768 created "2023-01-06" @default.
- W4313447768 creator A5020972219 @default.
- W4313447768 date "2022-12-30" @default.
- W4313447768 modified "2023-10-18" @default.
- W4313447768 title "Varsovian models $omega$" @default.
- W4313447768 doi "https://doi.org/10.48550/arxiv.2212.14878" @default.
- W4313447768 hasPublicationYear "2022" @default.
- W4313447768 type Work @default.
- W4313447768 citedByCount "0" @default.
- W4313447768 crossrefType "posted-content" @default.
- W4313447768 hasAuthorship W4313447768A5020972219 @default.
- W4313447768 hasBestOaLocation W43134477681 @default.
- W4313447768 hasConcept C114614502 @default.
- W4313447768 hasConcept C121332964 @default.
- W4313447768 hasConcept C2779557605 @default.
- W4313447768 hasConcept C33923547 @default.
- W4313447768 hasConcept C62520636 @default.
- W4313447768 hasConceptScore W4313447768C114614502 @default.
- W4313447768 hasConceptScore W4313447768C121332964 @default.
- W4313447768 hasConceptScore W4313447768C2779557605 @default.
- W4313447768 hasConceptScore W4313447768C33923547 @default.
- W4313447768 hasConceptScore W4313447768C62520636 @default.
- W4313447768 hasLocation W43134477681 @default.
- W4313447768 hasOpenAccess W4313447768 @default.
- W4313447768 hasPrimaryLocation W43134477681 @default.
- W4313447768 hasRelatedWork W1978042415 @default.
- W4313447768 hasRelatedWork W2100690540 @default.
- W4313447768 hasRelatedWork W2741667876 @default.
- W4313447768 hasRelatedWork W3086542228 @default.
- W4313447768 hasRelatedWork W3107062430 @default.
- W4313447768 hasRelatedWork W3154043682 @default.
- W4313447768 hasRelatedWork W3177761684 @default.
- W4313447768 hasRelatedWork W2117813624 @default.
- W4313447768 hasRelatedWork W2523674989 @default.
- W4313447768 hasRelatedWork W64040078 @default.
- W4313447768 isParatext "false" @default.
- W4313447768 isRetracted "false" @default.
- W4313447768 workType "article" @default.