0# and elementary end extensions of Vk
Amir Leshem
Abstract
In this paper we prove that if k is a cardinal in L[0#], then there is an inner model M such that M |= (Vk,E) has no elementary end extension. In particular if 0# exists then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than aleph1 of uncountable cofinality in L[0#] is Mahlo in every strict inner model of L[0#].
Create a lesson
Related papers
Logarithmic--exponential preparation in sharply o-minimal structures
Gal Binyamini, Oded Carmon, Dmitry Novikov
Stoic Logic and Natural Term Logic
Clarence Lewis Protin
From raw Solvability Complexity Index proofs to Weihrauch degrees
Christopher Sorg
Existence of bases implies the axiom of choice, a foundation-free proof
Gabriel Fernandes, Renan Maneli Mezabarba, Vinicius de Oliveira Rodrigues
Every countable meet-continuous lattice is Scott sober
Xiaoquan Xu, Wei Ji
A minimal type of Morley rank ω in a partial differential field
Piotr Kowalski