Notre Dame Journal of Formal Logic

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

Farmer Schlutzenberg

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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], (δ+)M and (ε+)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.

Article information

Notre Dame J. Formal Logic, Volume 59, Number 4 (2018), 599-604.

Received: 22 October 2015
Accepted: 21 September 2016
First available in Project Euclid: 12 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E45: Inner models, including constructibility, ordinal definability, and core models

inner model ordinal definable comparison


Schlutzenberg, Farmer. A Long Pseudo-Comparison of Premice in $L[x]$. Notre Dame J. Formal Logic 59 (2018), no. 4, 599--604. doi:10.1215/00294527-2018-0012.

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