Cotolerant sequence
Encyclopedia
In mathematical logic
, a cotolerant sequence is a sequence
of formal theories
such that there are consistent extensions
of these theories with each 
is cointerpretable
in
. Cotolerance naturally generalizes from sequences of theories to trees of theories.
This concept, together with its dual concept of tolerance, was introduced by Japaridze in 1992, who also proved that, for Peano arithmetic and any stronger theories with effective axiomatizations, tolerance is equivalent to
-consistency.
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
, a cotolerant sequence is a sequence
of formal theories
Formal theory
Formal theory can refer to:* Another name for a theory which is expressed in formal language.* An axiomatic system, something representable by symbols and its operators...
such that there are consistent extensions
of these theories with each is cointerpretableCointerpretability
In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when the language of S can be translated into the language of T in such a way that S proves every formula whose translation is a theorem of T...
in
. Cotolerance naturally generalizes from sequences of theories to trees of theories.This concept, together with its dual concept of tolerance, was introduced by Japaridze in 1992, who also proved that, for Peano arithmetic and any stronger theories with effective axiomatizations, tolerance is equivalent to
-consistency.