ON THE INCOMPLETENESS OF A DESCENDING CHAIN OF EXTENSIONS OF IMPLICATIONAL S5 | Zendy

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ON THE INCOMPLETENESS OF A DESCENDING CHAIN OF EXTENSIONS OF IMPLICATIONAL S5

Author(s) -

Ulrich Dolph

Publication year - 1992

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.19920380129

Subject(s) - axiom , fragment (logic) , chain (unit) , class (philosophy) , mathematics , computer science , arithmetic , discrete mathematics , algorithm , artificial intelligence , physics , geometry , astronomy

C5.ω is obtained by adding, schematically, to the strict‐implicational fragment C5 of S5 the axiom (( p → q ) → ( q → p )) → ( q → p ). This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper (same Zeitschrift 31 (1985), 201‐208).

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