A first-order sentence is a formula with no free variables, so its truth in a structure is independent of a variable assignment.
An existential sentence has a block of existential quantifiers followed by a quantifier-free formula. Empty blocks are allowed. These sentences are preserved when a first-order structure embeds into another structure.
Ancestors (6)
Incoming links (118)
- Assignment in a first-order structure
- Bounded arithmetic sentence
- Canonical models of complete theories are prime
- Complete omega-consistent arithmetic theories are sound
- Complete one-consistent theories can prove false sentences
- Decidable theory
- Distinct witnesses from incompatible unary predicates
- Elementary equivalence
- Existential quantification
- Existential second-order logic
- Fagin's theorem
- Finite axiomatization
- First-order sentence
- First-order variable assignment
- Full semantics for second-order logic
- Full set of first-order sentences
- Herbrand model
- Herbrand's theorem
- Involution with exactly one fixed point
- Iterated provability collapse implies the original theorem
- Logical fixed point
- Mathematical logic
- Maximal consistency of a first-order theory
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- Refutable sentences have the consistency nonprovability statement
- Second-order logic
- Semantic consequence under an assignment
- Sentence (mathematical logic)
- Skolem normal form
- Uniform substitution in modal logic
- Universal consequences of a theory
- Universal quantification
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