Embedding Logics into Product Logic

@article{Baaz1998EmbeddingLI,
  title={Embedding Logics into Product Logic},
  author={Matthias Baaz and Petr H{\'a}jek and David Svejda and Jan Kraj{\'i}cek},
  journal={Studia Logica},
  year={1998},
  volume={61},
  pages={35-47}
}
We construct a faithful interpretation of Lukasiewicz's logic in the product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable. We prove a completeness theorem for the product logic extended by a unary connective 4 of Baaz 1]. We show that GG odel's logic is a sublogic of this extended product logic. We also prove NP-completeness of the set of propositional formulas satissable in product logic (resp. in GG… CONTINUE READING
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