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If in addition C satisfies (3) we say that it is a finitary consequence operation.
In order to simplify the notation we denote this consequence operation by CL.
He also contributed to general metamathematics (the theory of consequence operation) and intuitionistic logic.
In other words, the theories of L are the closed sets of the consequence operation C⊢L on the set of L-formulas.
Logicians of this school also made precise many important metalogical concepts, including those of the logical matrix, consequence operation, deductive system and model.
To achieve this, we employ an abstract consequence operation to "look beneath the water level", generalising the minimal inconsistent set concept and the related free formula notion.
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Abstract consequence operations are known as closure operators in universal algebra and lattice theory, for instance.
Consequence operations are present not only in logic but in many areas of mathematics.
In consequence, service operation and management needs to be redefined to put customers at the heart of daily operations.
Serafina, heading north, runs into another consequence of Operation Gatekeeper: the dependence on sometimes rapacious smugglers who act as guides through the rough terrain.
As a consequence, the operation cost decreases and money is saved.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com