Henkin construction
E446858
Henkin construction is a model-building technique in first-order logic that extends a theory with new constants to ensure every consistent set of sentences has a model, thereby proving completeness.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
method in first-order logic
ⓘ
model construction method ⓘ technique in mathematical logic ⓘ |
| alternativeTo |
semantic tree methods for completeness
ⓘ
tableau-based completeness proofs ⓘ |
| appliesTo |
arbitrary first-order theories
ⓘ
countable first-order languages ⓘ |
| assumes | consistency of the initial theory ⓘ |
| basedOn | extension of a theory by new constants ⓘ |
| coreIdea |
add constants to witness existential quantifiers
ⓘ
build a model whose domain is formed from terms of the extended language ⓘ |
| ensures | every consistent set of first-order sentences has a model ⓘ |
| field |
mathematical logic
ⓘ
model theory ⓘ proof theory ⓘ |
| framework | classical logic ⓘ |
| generalizes | canonical model construction for propositional logic ⓘ |
| guarantees | existence of a model for any consistent first-order theory ⓘ |
| historicalPeriod | 20th century ⓘ |
| influenced |
modern presentations of completeness proofs
ⓘ
textbook expositions of first-order logic ⓘ |
| introduces |
Henkin constants
NERFINISHED
ⓘ
Henkin witnesses NERFINISHED ⓘ |
| methodStep |
add Henkin axioms for existential sentences
ⓘ
define a term model using equivalence classes of terms ⓘ extend the language with new constant symbols ⓘ extend the theory to a maximally consistent set ⓘ interpret function symbols by term operations ⓘ interpret predicate symbols by satisfaction in the maximally consistent set ⓘ |
| namedAfter | Leon Henkin NERFINISHED ⓘ |
| preserves | consistency of the theory ⓘ |
| relatedTo |
Gödel completeness theorem
NERFINISHED
ⓘ
Lindenbaum lemma NERFINISHED ⓘ Skolemization NERFINISHED ⓘ canonical model construction ⓘ term model ⓘ |
| requires |
classical first-order logic with equality (in standard presentations)
ⓘ
enumeration of all sentences of the language ⓘ |
| satisfies | witness property for existential formulas ⓘ |
| usedFor |
building models of first-order theories
ⓘ
constructing term models ⓘ proving Gödel completeness theorem ⓘ proving completeness theorems ⓘ |
| usedIn |
first-order logic
ⓘ
proof of strong completeness for first-order logic ⓘ proofs of compactness theorem via completeness ⓘ |
| yields | Henkin model NERFINISHED ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.