A Long Pseudo-Comparison of Premice in L[x]

Notre Dame Journal of Formal Logic 59 (4):599-604 (2018)
  Copy   BIBTEX

Abstract

A significant open problem in inner model theory is the analysis of HODL[x] as a strategy premouse, for a Turing cone of reals x. We describe here an obstacle to such an analysis. Assuming sufficient large cardinals, for a Turing cone of reals x there are proper class 1-small premice M,N, with Woodin cardinals δ,ε, respectively, such that M|δ and N|ε are in L[x], M and N are countable in L[x], and the pseudo-comparison of M with N succeeds, is in L[x], and lasts exactly ω1L[x] stages. Moreover, we can take M=M1, the minimal iterable proper class inner model with a Woodin cardinal, and take N to be M1-like and short-tree-iterable.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 98,072

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

In inner models with Woodin cardinals.Sandra Müller & Grigor Sargsyan - 2021 - Journal of Symbolic Logic 86 (3):871-896.
The largest countable inductive set is a mouse set.Mitch Rudominer - 1999 - Journal of Symbolic Logic 64 (2):443-459.
Definability of types, and pairs of o-minimal structures.Anand Pillay - 1994 - Journal of Symbolic Logic 59 (4):1400-1409.
Inner model operators in L.Mitch Rudominer - 2000 - Annals of Pure and Applied Logic 101 (2-3):147-184.
Downward transfer of satisfiability for sentences of L 1,1.Jerome Malitz - 1983 - Journal of Symbolic Logic 48 (4):1146-1150.
Projective Games on the Reals.Juan P. Aguilera & Sandra Müller - 2020 - Notre Dame Journal of Formal Logic 61 (4):573-589.
Generic coding with help and amalgamation failure.Sy-David Friedman & Dan Hathaway - 2021 - Journal of Symbolic Logic 86 (4):1385-1395.
Dynamic ordinal analysis.Arnold Beckmann - 2003 - Archive for Mathematical Logic 42 (4):303-334.

Analytics

Added to PP
2018-10-12

Downloads
13 (#1,221,096)

6 months
3 (#1,419,365)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

HOD L(ℝ) is a Core Model Below Θ.John R. Steel - 1995 - Bulletin of Symbolic Logic 1 (1):75-84.

Add more references