Exact(1)
The effect of the antinomy is that it is impossible to have an abstraction operation φ {x | φ } mapping injectively any concept (property) φ into its extension (the class of all x such that φ(x)) (i.e., so that if the classes defined by φ and ψ are equal, then φ(a)↔ ψ(a), for every object a).
Similar(58)
Last fall, the organization suspended its women's sewing cooperative, an extension of the class that allowed women to sell their goods and receive 50 percent of the profits.
These two approaches are not only intensionally divergent; they also disagree on the extension of the class of formal consequences.
The Weyl almost periodic function is an extension of the class of Stepanov almost periodic function.
As an important extension of the class of contractive mappings, the class of weakly contractive mappings was introduced by Alber and Guerre-Delabriere [1].
An extension of the class of ln,p-symmetric distributions to the class of skewed ln,p-symmetric distributions has been derived in ([Arellano-Valle and Richter 2012]).
By using some extension of the class of unknown functions, the proofs are based on the solvabilities of equivalent inverse problems for transport-like equation.
On using some extension of the class of functions λ, the overdetermined Problem 1 is replaced by a determined one (Problem 2 in Section 3.1).
As an extension of the class of ((alpha,psi -Meir-Keeler-Khan single-valpha,psi -Meir-Keeler-Khandjel et alpha,psi -Meir-Keeler-Khansi))-Meir-Keeler-Khalpha,psi -Meir-Keeler-Khanresented.
Plainly, such an approach must yield a very different account of the extension of the class of abstract objects from a directly metaphysical approach.[19] Among non-particulars objects, the emphatic focus on properties or attributes, along with a corresponding neglect or downgrading of kinds, has a history going back to Hume and before Hume, indeed, to Locke's 'simple qualities'.
We do not conclude that human beings must be treated this way; the recognition that they must is already part of the meaning of the concept (Diamond 1978; Gleeson 2008).[13] This thick, normative concept of human being is not a biological one, and need not have the same extension as the class of Homo sapiens.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com