Chains of End Elementary Extensions of Models of Set Theory

1996/11/13 by Andrés Villaveces, Villaveces, Andres · 1 citation
Mathematics · Computer Science · #Advanced Topology and Set Theory #Mathematical and Theoretical Analysis #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.math/9611209

Abstract

Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained that way (`Unfoldable cardinals') behave as a `boundary' between properties consistent with `V=L' and existence of indiscernibles. We also provide an `embedding characterisation' of the unfoldable cardinals and study their preservation and destruction by various different forcings.

Cited by

• Eventual Capture on a Measurable Cardinal

Related

• Extendible cardinals, and Laver-generic large cardinal axioms for extendibility
• Heights of Models of ZFC and the Existence of End Elementary Extensions
• Large cardinals beyond HOD
• Model-theoretic characterizations of large cardinals (Re)²visited
• The Landscape of Large Cardinals