Regular Languages and Model Theory 33: Tail-Head Functions
Because nonstandard models of WS1S are closed under finite modifications, the interesting part of their behavior takes place in infinite cuts: places between the copies of Z in their first-order parts. In this video, I introduce some language for talking about this behavior and prove some basic results.
I talk more about the sorts of trouble you can get into with the axiom of choice looking at these sorts of equivalence classes in my video "A Peculiar Connection between the Axiom of Choice and Infinite Hat Games", • A Peculiar Connection between the Axiom of...
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