The foundation axiom and elementary self-embeddings of the universe
Ali Sadegh Daghighi, Mohammad Golshani, Joel David Hamkins and, Emil Je\v{r}\'abek
TL;DR
This paper explores how the foundation axiom and anti-foundation axioms influence the existence and nature of elementary self-embeddings within the set-theoretic universe.
Contribution
It analyzes the impact of different axioms on the properties and existence of elementary self-embeddings in set theory.
Findings
Foundation axiom restricts certain self-embeddings
Anti-foundation axioms allow new types of embeddings
Results clarify the relationship between axioms and universe automorphisms
Abstract
We consider the role of the foundation axiom and various anti-foundation axioms in connection with the nature and existence of elementary self-embeddings of the set-theoretic universe.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Computability, Logic, AI Algorithms · Advanced Topology and Set Theory