Routledge Dictionary of Language and Linguistics
isomorphism [Grk 
‘form, shape’]
1 In set theory, fundamental concept of a general structural theory that denotes structural equivalence in regard to certain relations between elements of two (or more) sets. Isomorphism can be comprehended with the help of bijective mapping (
function) that maintains the structure: for example, the set of natural numbers {1,2,3,4,…} is isomorphic to the set of natural even numbers {2,4,6,…} with regard to the relation of ‘greater than’ (notation: >), since the function f(n)=2xn is a subjective function between the sets in question, and n> m is equivalent to f(n)>f(m).
References
formal logic, set theory
2 Concept introduced by J.Kuryłowicz (1949) into linguistics that refers to the structural parallelism between different levels of description (phonology, morphology, etc.). The assumption of isomorphism is meant to justify the use of the same investigative or descriptive methods, a hypothesis that has been only partly confirmed in the transfer of phonological concepts (distinctive features) to semantic concepts (componential analysis).
References
Kuryłowicz, J.
1949. La notion de l’isomorphisme. TCLC 5. 48–60.
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