کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6424848 1633492 2011 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Finite axiomatizability in Łukasiewicz logic
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
Finite axiomatizability in Łukasiewicz logic
چکیده انگلیسی

We classify every finitely axiomatizable theory in infinite-valued propositional Łukasiewicz logic by an abstract simplicial complex (V,Σ) equipped with a weight function ω:V→{1,2,…}. Using the Włodarczyk-Morelli solution of the weak Oda conjecture for toric varieties, we then construct a Turing computable one-one correspondence between (Alexander) equivalence classes of weighted abstract simplicial complexes, and equivalence classes of finitely axiomatizable theories, two theories being equivalent if their Lindenbaum algebras are isomorphic. We discuss the relationship between our classification and Markov's undecidability theorem for PL-homeomorphism of rational polyhedra.

► Finitely axiomatizable Łukasiewicz theories are classified by rational polyhedra. ► Rational polyhedra are classified by weighted abstract simplicial complexes. ► Regular triangulations of rational polyhedra correspond to nonsingular fans.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 162, Issue 12, December 2011, Pages 1035-1047
نویسندگان
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