Notre Dame Journal of Formal Logic 46 (2):147-164 (2005)

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 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 , then p can be embedded in the prefix of θ. This strengthens a theorem of Walkoe
Keywords first-order prefix   expressive power
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DOI 10.1305/ndjfl/1117755146
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