TotOrd is just the axioms of totally ordered sets
I am not sure how to create a sentence that characterizes infinite sets with 2 endpoints
2026-03-31 17:46:39.1774979199
Find a first order sentence that characterizes infinite totally ordered sets
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There is no such statement: any finite totally ordered set should be a model of $\mathcal{TotOrd} \cup \{\neg \phi\}$, but if theory has finite models of arbitrary large size then it has an infinite model too, so there will be some infinite totally ordered set that $\nvDash \phi$.