An effective characterization of the alternation hierarchy in two-variable logic [article]

Andreas Krebs, Howard Straubing
2012 arXiv   pre-print
We characterize the languages in the individual levels of the quantifier alternation hierarchy of first-order logic with two variables by identities. This implies decidability of the individual levels. More generally we show that the two-sided semidirect product of a decidable variety with the variety J is decidable.
arXiv:1205.4802v1 fatcat:aj7tzkfpmzg7vjio6r65ovk3mm