enumerable language
51Decidability (logic) — In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas. Logical systems such as propositional logic are decidable if membership in their… …
52Machine that always halts — In computability theory, a machine that always halts also called a decider (Sipser, 1996) or a total Turing machine (Kozen, 1997) is a Turing machine that halts for every input. Because it always halts, the machine is able to decide whether a… …
53Undecidable problem — In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct an algorithm that leads to a yes or no answer the problem is not decidable.A decision problem is any …
54Theory (mathematical logic) — This article is about theories in a formal language, as studied in mathematical logic. For other uses, see Theory (disambiguation). In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually… …
55Model theory — This article is about the mathematical discipline. For the informal notion in other parts of mathematics and science, see Mathematical model. In mathematics, model theory is the study of (classes of) mathematical structures (e.g. groups, fields,… …
56Arithmetical hierarchy — In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical. The… …
57Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …
58Fixed-point combinator — Y combinator redirects here. For the technology venture capital firm, see Y Combinator (company). In computer science, a fixed point combinator (or fixpoint combinator[1] ) is a higher order function that computes a fixed point of other functions …
59Proof sketch for Gödel's first incompleteness theorem — This article gives a sketch of a proof of Gödel s first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses which are discussed as needed during the sketch. We will assume for the… …
60Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… …
