Robinson's Joint Consistency Theorem states that two first-order theories are jointly consistent, meaning they can be combined without contradiction, whenever each is individually consistent and they agree on every sentence expressible in the language common to both. Named for Abraham Robinson, it is a foundational model-theoretic result closely related to the Craig Interpolation Theorem, from which it follows.
Facts
StatementIf two theories are each consistent and they agree on every sentence expressible in the language common to both, then the union of the two theories is also consistent. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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In Branch
Source Robinson's joint consistency theorem, Wikipedia
Sources
1. Robinson's joint consistency theorem, Wikipedia
Lead section, classical formulation
If T1 and T2 are consistent and the intersection T1 and T2 is complete (in the common language of T1 and T2), then the union T1 and T2 is consistent.
In Branch: Logic and Foundations, Lead sentence
nt consistency theorem is an important theorem of mathematical logic.
In Group: Mathematical Logic and Model Theory, Lead section
joint consistency theorem is an important theorem of mathematical logic. It is related to Craig interpolation and Beth
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