Given a first-order structure \(M\), we say that an invariant \(I(M)\) reconstructs \(M\) if knowing \(I(M)\) is enough to know \(M\) up to a suitable notion of equivalence (called bi-interpretation). By a result attributed to Coquand, any \(\omega\)-categorical structure \(M\) is reconstructed by its automorphism group equipped with the topology of pointwise convergence. A natural question to ask is under which circumstances one can disregard topology and determine \(M\) (up to bi-interpretation) from its automorphism group — or even its endomorphism monoid — as purely algebraic objects. Lascar gave a partial answer to this question in 1982, showing that when \(M\) has a property called \(G\)-finiteness, \(M\) is reconstructed by its endomorphism monoid (without topology). In this talk, I will discuss some aspects of this result.
Reconstructing an ω-categorical structure from its endomorphism monoid
24.04.2024 11:30 - 13:00
Organiser:
KGRC
Location: