“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 48 |
|
||||
| Abstract: | |||||
|
Let L and N be propositional languages over Basic Propositional Calculus, and M=L∩N. We prove two different but interrelated interpolation theorems. First, suppose that II is a sequent theory over L, and Σ∪{ C⇒ C′} is a set of sequents over N, such that II, Σ\vdash C ⇒ C′. Then there is a sequent theory Φ over M such that Π\vdash Φ and Φ,Σ\vdash C⇒ C′. Second, let A be a formula over L,
and C1,C2 be formulas over N, such that A∧C1\vdash C2. Then there exists a formula B over M
such that A\vdash B and B∧C1\vdash C2.
Download TeX format |
|||||
| back to top | |||||
