On the extension of intuitionistic propositional logic with Kreisel-Putnam's and Scott's schemes
P Minari�- Studia Logica, 1986 - Springer
Studia Logica, 1986•Springer
Let SKP be the intermediate prepositional logic obtained by adding to I (intuitionistic pl) the
axiom schemes: S=((ℸ ℸ α→ α)→ α∨ ℸ α)→ ℸ α∨ ℸℸ α (Scott), and KP=(ℸ α→ β∨ γ)→(ℸ
α→ β)∨(ℸ α→ γ)(Kreisel-Putnam). Using Kripke's semantics, we prove: 1) SKP has the finite
model property; 2) SKP has the disjunction property. In the last section of the paper we give
some results about Scott's logic S= I+ S.
axiom schemes: S=((ℸ ℸ α→ α)→ α∨ ℸ α)→ ℸ α∨ ℸℸ α (Scott), and KP=(ℸ α→ β∨ γ)→(ℸ
α→ β)∨(ℸ α→ γ)(Kreisel-Putnam). Using Kripke's semantics, we prove: 1) SKP has the finite
model property; 2) SKP has the disjunction property. In the last section of the paper we give
some results about Scott's logic S= I+ S.
Abstract
LetSKP be the intermediate prepositional logic obtained by adding toI (intuitionistic p.l.) the axiom schemes:S = ((ℸ ℸα→α)→α∨ ℸα)→ ℸα∨ ℸℸα (Scott), andKP = (ℸα→β∨γ)→(ℸα→β)∨(ℸα→γ) (Kreisel-Putnam). Using Kripke's semantics, we prove:
- 1) SKP has the finite model property;
- 2) SKP has the disjunction property.
In the last section of the paper we give some results about Scott's logic S = I+S.
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