{"paper":{"title":"Three Variables Suffice for Real-Time Specification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"James Worrell, Paul Hunter, Shahab Raza, Timos Antonopoulos","submitted_at":"2014-08-08T13:48:35Z","abstract_excerpt":"A natural framework for real-time specification is monadic first-order logic over the structure $(\\mathbb{R},<,+1)$---the ordered real line with unary $+1$ function. Our main result is that $(\\mathbb{R},<,+1)$ has the 3-variable property: every monadic first-order formula with at most 3 free variables is equivalent over this structure to one that uses 3 variables in total. As a corollary we obtain also the 3-variable property for the structure $(\\mathbb{R},<,f)$ for any fixed linear function $f:\\mathbb{R}\\rightarrow\\mathbb{R}$. On the other hand, we exhibit a countable dense linear order $(E,<"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1851","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}