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definable-saturated

Elliot Glazer

Palomar Registrypalomar/PALOMAR-2026-09-19-000005Sep 19, 2026math.LOscore 0

A Lean 4 formalization of the relative consistency of ZFC + CH together with the following assertion. There is a countably saturated elementary extension of the natural-number arithmetic structure of cardinality aleph one; all such set-sized presentations are isomorphic; and no such presentation is ordinal definable. The class is defined without parameters. Removing CH from the asserted theory gives a consistent negative answer to MathOverflow question 382009 about definability up to isomorphism versus an ordinal-definable copy. Every notion in the final sentence is internal to the…

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