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Ernest Schimmerling

Publications and source records attributed to Ernest Schimmerling.

6 recordsLinked to original sources
arXiv2026

Maximal Prikry Sequences

In this paper we investigate the covering machinery of the Jensen-Steel core model $K$, under the hypothesis that there is no inner model with a Woodin cardinal. In an earlier work, Mitchell and the first author showed that if $ν>ω_2$ is a regular cardinal in $K$ but a singular ordinal in $V$, then $ν$ is a measurable cardinal in $K$. In this article, we further show that under certain circumstances, there exists a maximal Prikry sequence $C$ for a measure on $ν$ in $K$. The first author shows that the anti-large cardinal hypothesis is necessary. In a more restrictive setting, we prove that every subset of $ν$ with size $<|ν|$ can be covered by a set in $K[C]$ with size $<|ν|$. Benhamou and the first author show that the result is optimal.

math.LO↗
arXiv2013

Some Calkin algebras have outer automorphisms

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.

math.LO↗
arXiv1997

The maximality of the core model

If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K computes successors of weakly compact cardinals correctly. o K^c is an iterate of K. o (with Mitchell) If alpha is a cardinal > aleph_1, then K-restriction-alpha is universal for mice of height alpha. Other results in this paper, when combined with work of Woodin, imply: o If square-kappa-finite fails and kappa is a singular, strong limit cardinal, then Inductive Determinacy holds. o If square-kappa-finite fails and kappa is a weakly compact cardinal, then L(R)-determinacy holds.

math.LO↗
arXiv1997

The covering lemma up to a Woodin cardinal

A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa. Assume that there is no inner model with a Woodin cardinal and that every set has a sharp. Let K be the core model. Assume that kappa is a countably closed cardinal and that alpha is a successor cardinal of K with kappa < alpha < kappa^+. Then cf( alpha ) = kappa. In particular, K computes successors of countably closed singular cardinals correctly. (The hypothesis of countable closure is not required; see "Weak covering without countable closure", W. J. Mitchell and E. Schimmerling, Math. Res. Lett., Vol. 2, No. 5, Sept. 1995.)

math.LO↗
arXiv1997

The Jensen covering property

An optimal extension of the Jensen covering lemma, within the limits imposed by Prikry forcing, is proved. If L[E] is an "iterable" weasel with no measurable cardinals, then either L[E] has "indiscernibles", or every uncountable set of ordinals is contained in a set in L[E] of the same cardinality. (The terms "iterable" and "indiscernibles" are made precise in the paper.) Most importantly, there is no hypothesis explicitly limiting the large cardinals which are consistent in L[E].

math.LO↗