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First-Order logic and its Infinitary Quantifier Extensions over Countable Words
[article]
2021
arXiv
pre-print
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as boolean closure of existential fragment of FO via a strengthening of Simon's theorem about piecewise testable languages. We propose a new extension of FO which admits infinitary quantifiers to reason about the inherent infinitary properties of countable words.
arXiv:2107.01468v1
fatcat:k5zie3jeibgkrfapfgqzdoazhe