A Normal form Theorem for Recursive Operators in Iterative Combinatory Spaces

✍ Scribed by D. Skordev

• Publisher: John Wiley and Sons
• Year: 1978
• Tongue: English
• Weight: 473 KB
• Volume: 24
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19780240803

✦ Synopsis

A XORMAL FORM THEOREM FOR RECURSIVE OPERATORS

Lemma 2. All elements of 9 ? and the element I are perfect. If E and rj are perfect elements of 9, then (t, q ) is also perfect.

Proof. Obvious from the definition.

L e m m a 3. Let [ be a perfect element of 9. Then Vp(L(p7, [) = 9 & R ( [ . y ) = 9).

Proof. If x is an arbitrary element of V, then L(q, 1') z = L(yx, 5. ) = L ( I , 5. ) 92 = I q x = q x , R((, q ) x = R ([x, cpx) = R((x, I) p x = Iplx = 9 ~. l ) lye shall use the terminology and the notations from [I] without expIicit referenres.