Compactness in first-order Godel logics
Massoud Pourmahdian, N. R. Tavana · Journal of Logic and Computation · 2012
Our aim in this article is twofold. First, for an arbitrary closed subset V of [0,1] containing both 0 and 1, the compactness theorem for the Gödel logic GV is investigated. Next, following Cintula and Navara (2004, Fuzzy sets and systems, 143, 59–73) and Tavana et al. (2012, Logic J. IGPL, 20, 254–265), for any subset K of [0,1], the notions of K-satisfiability and K-compactness are introduced for the standard first-order Gödel logic Gℝ. It is shown that whenever K is closed, the K-compactness fails for Gℝ if and only if K is infinitely countable and 1 ∉ K.