Seyed Mohammad Amin Khatami

Department of Computer Science, Birjand University of Technology

Abstract. One of the nice properties of the first-order logic is the compactness of satisfiability. It states that a finitely satisfiable theory is satisfiable. Here, some new results are given around the compactness of satisfiability in Hájek Basic logic. It is shown that there are topologies on [0, 1] and [0, 1]² for which the interpretation of all logical connectives of the Basic logic are continuous. Furthermore, a topology on first-order structures is introduced for any similarity relation, and then by the same ideas as in the continuous logic, the results around the compactness of satisfiability for Basic logic are extended.