caa a22 4500 465779530 CHVBK 20180323111951.0 cr unu---uuuuu 170327e19900601xx s 000 0 eng 10.1007/BF00935597 doi (NATIONALLICENCE)springer-10.1007/BF00935597 Hughes G. Victoria University of Wellington, Wellington, New Zealand aut Every world can see a reflexive world [Elektronische Daten] [G. Hughes] Let ℭ be the class of frames satisfying the condition $$\forall x\exists y(Ry \wedge yRy)$$ ("every world can see a reflexive world”). LetKMT be the system obtained by adding to the minimal normal modal systemK the axiom $$M((Lp_1 \supset p_1 ) \wedge ... \wedge (Lp_n \supset p_n ))$$ for eachn ⩾ 1. The main results proved are: (1)KMT is characterized by ℭ. (2)KMT has the finite model property. (3) There are frames forKMT which are not in ℭ, but allfinite frames forKMT are in ℭ. (4)KMT is decidable. (5)KMT is not finitely axiomatizable. (6) The class of all frames forKMT is not definable by any formula of first-order logic. (7) 〈W, R〉 is a frame forKMT iff for everyx εW, the worlds thatx can see form a sub-frame which is not finitely colourable. Polish Academy of Sciences, 1990 Studia Logica Kluwer Academic Publishers 49/2(1990-06-01), 175-181 0039-3215 49:2<175 1990 49 11225 https://doi.org/10.1007/BF00935597 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00935597 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hughes G. Victoria University of Wellington, Wellington, New Zealand aut NATIONALLICENCE 773 0- Studia Logica Kluwer Academic Publishers 49/2(1990-06-01), 175-181 0039-3215 49:2<175 1990 49 11225 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer