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Formal systems, equivalence of

From Encyclopedia of Mathematics
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Two formal systems (cf. Formal system) are called equivalent if the sets of expressions that are deducible in these systems are identical. More precisely, two formal systems and are equivalent if and only if the following conditions are satisfied: 1) every axiom of is deducible in ; 2) every axiom of is deducible in ; 3) if an expression follows immediately from expressions by virtue of a derivation rule of , and are deducible in , then is also deducible in ; and 4) the same as 3) with and interchanged.

How to Cite This Entry:
Formal systems, equivalence of. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Formal_systems,_equivalence_of&oldid=41452
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article