Definition of Metatheorem. Meaning of Metatheorem. Synonyms of Metatheorem

- a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved...
- In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly...
- φ0. We also use repeatedly the method of the hypothetical syllogism metatheorem as a shorthand for several proof steps. (1) φ 0 {\displaystyle \varphi...
- Statements made in the metatheory about the theory are called metatheorems. A metatheorem is a true statement about a formal system expressed in a metalanguage...
- problems influenced mathematics for the rest of the 20th century. A metatheorem is defined as: "a statement about theorems. It usually gives a criterion...
- In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises...
- Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories....
- In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic...
- conclusion. In most logics, weakening is either an inference rule or a metatheorem if the logic doesn't have an explicit rule. Notable exceptions are: Relevance...
- the same basic thought (e.g. deduction theorem) must be proven as a metatheorem in Hilbert-style deduction system, while it can be declared explicitly...