Metatheory - University of Cambridge
Metatheory - University of Cambridge
Metatheory - University of Cambridge
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Contents 2<br />
The corresponding notions from pro<strong>of</strong>-theory are also properties <strong>of</strong> sentences.<br />
Thus we write:<br />
Γ ⊢ C<br />
to indicate that there is a TFL-pro<strong>of</strong> which starts with assumptions among Γ<br />
and ends with C on no further assumptions. If there is no such pro<strong>of</strong>, we write:<br />
Γ ⊬ C<br />
A special case <strong>of</strong> this notation is used when there is a TFL-pro<strong>of</strong> which starts<br />
with assumptions among Γ and ends with ‘⊥’ (i.e. with an absurdity). In this<br />
situation, we say that Γ ⊢ ⊥, or that Γ are jointly contrary. (I should note that<br />
‘⊥’ is not a primitive 0-place connective <strong>of</strong> TFL. Rather, ‘⊥’ shows up only in<br />
TFL’s pro<strong>of</strong>-theory. For more details, see fx C§26.7)
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