TL;DR
The paper discusses the ground axiom in set theory, asserting that the universe cannot be obtained by forcing over any inner model, and shows it is first-order expressible.
Contribution
It provides an analysis of the ground axiom, clarifying its first-order expressibility within set theory.
Findings
Ground axiom is first-order expressible
It characterizes the universe as not obtainable by forcing
Clarifies the logical status of the ground axiom
Abstract
The ground axiom is the assertion that the set-theoretic universe is not obtainable by forcing over any inner model. Although this appears at first to be a second-order assertion, it is actually first-order expressible in the language of set theory. This article is the extended abstract for a talk at the 2005 Workshop in Set Theory at the Mathematisches Forschungsinstitut Oberwolfach.
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Taxonomy
TopicsPhilosophy and Theoretical Science · Philosophy, Science, and History · History and Theory of Mathematics