Abstract
We investigate the expressive power of fragments of first-order logic that are defined in terms of prefixes. The main result establishes a strict hierarchy among these fragments over the signature consisting of a single binary relation. It implies that for each prefix p, there is a sentence $\phi_p$ in prenex normal form with prefix p, over a single binary relation, such that for all sentences θ in prenex normal form, if θ is equivalent to $\phi_p$, then p can be embedded in the prefix of θ. This strengthens a theorem of Walkoe.
Citation
Eric Rosen. "On the First-Order Prefix Hierarchy." Notre Dame J. Formal Logic 46 (2) 147 - 164, 2005. https://doi.org/10.1305/ndjfl/1117755146
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