Examples of reducibility

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The addition of a terminal object causes all approaches to prove strong normalization via reducibility methods to fail.
Instead, we implicitly show that the conditions for reducibility are met.
We then shortly hint at a severe technical difficulty in adapting the standard strong normalization proofs which use the so called reducibility method.
It is a set of vectors of pairs, each pair consisting of a sequent and (possibly) a reducibility candidate.
What conventionalism contested, however, was not the rationality of science, but its reducibility to a mechanical process.
For non-symmetric matrices, the reducibility is not guaranteed to be preserved.
We introduce a notion of reducibility of representations of topological spaces and study some basic properties of this notion for domain representations.
In other words, we want to know that "reaching under a constructor" is a safe operation from the reducibility point of view.
A pre-model is a many-valued model whose truth values are reducibility candidates, that is, sets of proof-terms.
But, reducibility requires a number of other constraints as well.
We are now ready to define reducibility candidates.
The primary contributions of this paper are the introduction of a simplifying representation of friction and formal tests for kinematic reducibility.
Despite supervenience, if explanatory reducibility fails in principle for some entity, then it is emergent.
The presence of expansionary, context sensitive rewrite rules means that the reducibility predicates must be modified slightly.
We will show that the reducibility of function symbol headed terms follows from the reducibility of their arguments.
The perpetuality analysis has allowed us to obtain a 'pure' reducibility proof.
Indeed, since -expansion means our reduction is typed, it is convenient for the reducibility candidates to contain well-typed terms.
The proof uses the standard method of reducibility candidates.
It permits only the use of clear concepts whose clarity results from their reducibility to other clear concepts within the same system.
Kincaid rejects this as a conflation of theoretical reducibility and explanatory reducibility (p. 39).

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