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If $T$ is a theory of $\mathcal{L}$ then it is consistent iff there is some model $\mathcal{M}$ of $\mathcal{L}$ such that $\mathcal{M}\vDash T$ . If a theory is not consistent then it is inconsistent.
A slightly different definition is sometimes used, that $T$ is consistent iff $T\not\vdash\bot$ (that is, as long as it does not prove a contradiction). As long as the proof calculus used is sound and complete, these two definitions are equivalent.
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"consistent" is owned by Henry.
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inconsistent |
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Cross-references: definitions, complete, sound, Calculus, proof, contradiction, iff, theory
There are 64 references to this entry.
This is version 3 of consistent, born on 2002-08-28, modified 2002-09-04.
Object id is 3386, canonical name is Consistent2.
Accessed 14044 times total.
Classification:
| AMS MSC: | 03B99 (Mathematical logic and foundations :: General logic :: Miscellaneous) |
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Pending Errata and Addenda
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