same principles as the semantics of modal logic, but uses a different definition of satisfaction. An intuitionistic Kripke model is a triple , where is a partially ordered Kripke frame, and satisfies the following conditions: if p is a propositional variable, , and , then (persistency condition), if and only if and , if and only if or , if and only if for all , implies , not . Intuitionistic logic is sound and complete with respect to its Kripke semantics, and it has the Finite Model Property. Intuitionistic first-order logic Let L be a first-order language. A Kripke model of L is a triple , where is an intuitionistic Kripke frame, Mw is a (classical) L-structure for each node w ∈ W, and the following compatibility conditions hold whenever u ≤ v: the domain of Mu is included in the domain of Mv, realizations of function symbols in Mu and Mv agree on elements of Mu, for each n-ary predicate P and elements a1,...,an ∈ Mu: if P(a1,...,an) holds in Mu, then it holds in Mv. Given an evaluation e of variables by elements of Mw, we define the satisfaction relation : if and only if holds in Mw, if and only if and , if and only if or , if and only if for all , implies , not , if and only if there exists an such that , if and only if for every and every , . Here e(x→a) is the evaluation which gives x the value a, and otherwise agrees with e. Naming and Necessity The three lectures that form Naming and Necessity constitute an attack on the descriptivist theory of names. Kripke attributes variants of descriptivist theories to Frege, Russell, Wittgenstein, and John Searle, among others. According to descriptivist theories, proper names either are synonymous with descriptions, or have their reference determined by virtue of the name's being associated with a description or cluster of descriptions that an object uniquely satisfies. Kripke rejects both these kinds of descriptivism. He gives several examples purporting to render descriptivism implausible as a theory of how names get their references determined (e.g., surely Aristotle could have died at age two and so not satisfied any of the descriptions we associate with his name, but it would seem wrong to deny that he was still Aristotle). As an alternative, Kripke outlined a causal theory of reference,