Successor-Saturated Ordinals and Indefinite Tail Activation: A RED/DED Operator Extension of the Successor-Closed Sequence Lexicon

This paper strengthens a lexical hypothesis about ordinal meaning: encoding a position as FIRSTnecessarily encodes a successor position, and more strongly, encodes all successor positions inthe relevant sequence. Formally, sequence is defined as an index structure whose domain issuccessor-closed (or at minimum two-element) and whose semantic interface guarantees asuccessor for the initial index. Under the Successor-Closed Sequence Lexicon (SCSL), FIRST ⇒SECOND is not pragmatic enrichment but a lexical entailment/presupposition triggered by theordinal itself. Building on SCSL, I introduce Indefinite Tail Activation (ITA): when FIRSTanchors the beginning of a sequence, all remaining successor slots are introduced into thediscourse as an underspecified remainder that is canonically lexicalized as non-specificindefiniteness (“some / a few / others”). ITA is not derived from conversational reasoning; it is alexical interface consequence of successor saturation. The proposal is integrated into aRED/DED operator architecture: RED implements refinement along the successor chain (FIRST→ SECOND → THIRD → …), while DED implements controlled collapse from refined ordinalmicrostructure back to a coarse remainder expressed by non-specific indefinites. The resultingsystem intentionally changes the diagnostic landscape: standard implicature tests (cancellability,weakening under embedding) are not preserved, because successor availability and tailindefiniteness are lexical definedness/interface conditions rather than conversational inferences.The paper concludes with a replication-ready diagnostic set, a compact elicitation grid, andcomputational/neuroscientific implications for successor-chain activation and ordinal-drivendiscourse updates.