Identity and Definite Descriptions

Question 1

Atomic formulae of L=

Answer 1

All atomic formulae of L2 are atomic formulae of L=. Furthermore, if s and t are variables or constants then s = t is an atomic formla of L=.

Question 2

Formulae of L=

Answer 2

(i) All atomic formulae of L= are formulae of L=.
(ii) If φ and ψ are formulae of L= then ¬φ, (φ∧ψ), (φ∨ψ), (φ → ψ) and (φ ↔ ψ) are formulae of L=.
(iii) If v is a variable and φ is a formula then ∀vφ and ∃vφ are formulae of L=.
(iv) Nothing else is a formula of L=.

Question 3

Satisfaction in L=

Answer 3

As in the definition of satisfaction in L2 with the additional clause:
(ix) |s=t|αA =T iff |s|αA =|t|αA