Definition:First Order Logic with Identity
Jump to navigation
Jump to search
Definition
A system of first order logic with identity is a system of predicate logic with the following elements in its alphabet:
Connectives
\(\ds \land \) | \(\ds : \) | the conjunction sign | |||||||
\(\ds \lor \) | \(\ds : \) | the disjunction sign | |||||||
\(\ds \implies \) | \(\ds : \) | the conditional sign | |||||||
\(\ds \iff \) | \(\ds : \) | the biconditional sign | |||||||
\(\ds \neg \) | \(\ds : \) | the negation sign |
Quantifiers
\(\ds \exists \) | \(\ds : \) | the existential quantifier sign | |||||||
\(\ds \forall \) | \(\ds : \) | the universal quantifier sign |
Identity
\(\ds = \) | \(\ds : \) | the equality sign |
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 6$ Significance of the results