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The fact that M2 can be expanded to exactly two Tarskian models needs the Transfer Theorem, alluded to above.
The fact that M1 can be expanded to exactly one Tarskian model needs the so-called Transfer Theorem, Gupta and Belnap 1993, Theorem 2D.4.
(2) M2 can be expanded to exactly two Tarskian models, in one of which the sentence Tτ is true and in the other of which the sentence Tτ is false.
If we want to interpret Tx as 'x is true', then, given a ground model M, we would like to find an appropriate signification, or an appropriate range of significations, for T. Theorem 2.1 (1) M1 can be expanded to exactly one Tarskian model: in this model, the sentences (Tβ ∨ Tγ) and Tα are true, while the sentence ¬Tα is false.
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The pilot was expanded to 160 firms.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com