Year: 2016
Type: preprint
Abstract: It is shown that order-invariance of two-variable first-logic is decidable in the finite. This is an immediate consequence of a decision procedure obtained for the finite satisfiability problem for existential second-order logic with two first-order variables ($\mathrm{ESO}^2$) on structures with two linear orders and one induced successor. We also show that finite satisfiability is decidable on structures with two successors and one induced linear order. In both cases, so far only decidability for monadic $\mathrm{ESO}^2$ has been known. In addition, the finite satisfiability problem for $\mathrm{ESO}^2$ on structures with one linear order and its induced successor relation is shown to be decidable in non-deterministic exponential time.
Source: arXiv (Cornell University)
Authors: Zeume, Thomas, Harwath, Frederik
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G5013731361
OpenAlex ID: W2951229113