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 books.google.com In the first place we apply this technique to axiom systems for finite, concrete and sequential processes. It turns out that the number of actions is important for these sets to be [omega]complete. 

 books.google.com But if E were inconsistent, then I2 Q0 and I2 1Q0, for some 4,0 G FM(L), and
therefore, by (C), trans(Q0) and trans(14,0), which, by definition, is 1(trans(Q0)),
would both be tautologies, which is impossible. I 7.6 OmegaCompleteness in ... 

 books.google.com The concept of omegacompleteness which corresponds to the rules of GS is (
GOC) (for general omegacompleteness). (GOC) If w r G(Et > Pt) for every term t
of L, then w i G(VxPx), for any variable x. A GOC set is just a set with property ... 

 books.google.com Notable among these properties are omegacompleteness and omega
consistency. Omegacompleteness is the property a set of sentences has of
entailing every universal sentence whose particular instantiations it also entails. 

 books.google.com An alternative form of the completeness theorem is that every consistent
sentence is satisfiable. As usual our completeness ... Instead of the terminologies
of omega completeness, maximal consistency, and saturation , we give the
definitions ... 

 books.google.com Notice that in the completeness proof for propositional modal logic,
demonstration of the second fact requires a proof of (⊬∫), and the proof ... The
basic idea behind the method is to generalize the definition of omega
completeness so that it is ... 

 books.google.com Omegacompleteness, ^completeness  Tie property of formal systems of
arithmetic in which, far any formula A(x), from a deduction A (0), . . . ,A (n), .... it
follows that one can infer the formula VxA{x), where n is a constant signifying tic
natural ... 

 books.google.com 16, 18 Newton, I. 10 nonclassical logic see logic Novikov, N. 105 observation
statements 203—4, 215, 219, 229 omegacompleteness (tncompleteness) 103,
126 omegaconsistency (coconsistency) 103, 110—15, 128, 132—3 omega
model ... 

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