Editing Metamathematics (section)

===Tarski's definition of model-theoretic satisfaction===
{{main|T-schema}}
The T-schema or truth [[schema (logic)|schema]] (not to be confused with '[[Semantic theory of truth#Convention T|Convention T]]') is used to give an [[Recursive definition|inductive definition]] of truth which lies at the heart of any realisation of [[Alfred Tarski]]'s [[semantic theory of truth]]. Some authors refer to it as the "Equivalence Schema", a synonym introduced by [[Michael Dummett]].<ref name="Künne2005">{{cite book|author=Wolfgang Künne|title=Conceptions of truth|url=https://archive.org/details/conceptionsoftru0000kunn|url-access=registration|year=2003|publisher=Clarendon Press|isbn=978-0-19-928019-3|page=[https://archive.org/details/conceptionsoftru0000kunn/page/18 18]}}</ref>

The T-schema is often expressed in [[natural language]], but it can be formalized in [[Predicate logic|many-sorted predicate logic]] or [[modal logic]]; such a formalisation is called a '''''T-theory'''''.  T-theories form the basis of much fundamental work in [[philosophical logic]], where they are applied in several important controversies in [[analytic philosophy]].

As expressed in semi-natural language (where 'S' is the name of the sentence abbreviated to S):
'S' is true [[if and only if]] S

Example: 'snow is white' is true if and only if snow is white.