enumerable language
61Infinity — In mathematics, infinity is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: an infinite number of terms ) but it is a different type of number from the real numbers. Infinity is related to… …
62Algorithmically random sequence — Intuitively, an algorithmically random sequence (or random sequence) is an infinite sequence of binary digits that appears random to any algorithm. The definition applies equally well to sequences on any finite set of characters. Random sequences …
63Craig's theorem — In mathematical logic, Craig s theorem states that any recursively enumerable set of well formed formulas of a first order language is (primitively) recursively axiomatizable. This result is not related to the well known Craig interpolation… …
64Constructivism (mathematics) — In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct ) a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption,… …
65Theory — The word theory has many distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion.In science a theory is a testable model of the manner of interaction of a set of natural phenomena,… …
66Post's theorem — In computability theory Post s theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. Background The statement of Post s theorem requires several concepts relating to definability and… …
67Chaitin's constant — In the computer science subfield of algorithmic information theory, a Chaitin constant or halting probability is a real number that informally represents the probability that a randomly constructed program will halt. These numbers are formed from …
68Numbering (computability theory) — In computability theory a numbering is the assignment of natural numbers to a set of objects like rational numbers, graphs or words in some language. A numbering can be used to transfer the idea of computability and related concepts, which are… …
69Proof of impossibility — A proof of impossibility, sometimes called a negative proof or negative result , is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general. Often proofs of impossibility have put to rest decades or… …
70Countable set — Countable redirects here. For the linguistic concept, see Count noun. Not to be confused with (recursively) enumerable sets. In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of… …
