On the Recursion Theorem in Iterative Operative Spaces

摘要: The recursion theorem in abstract partially ordered algebras, such as operative spaces and others, is the most fundamental result of algebraic theory. primary aim present paper to prove this for iterative full generality. As an intermediate result, a new rather large class models combinatory logic obtained. Introduction. theory was advanced by L. Ivanov his thesis [3]; it continuation improvement original axiomatic study started D. Skordev with ([7], [9], [10]), which named also peculiar feature Ivanov's theory, well at all, way using partial order. More specifically, studies least fixed points certain called spaces, from view point mutual expressibility; respect (called first after classical Kleene), asserts completeness so i.e., existence expressibility expressible mappings spaces. notion space, proposed [4], consists necessary suppositions basic development up normal form theorem, defined means two natural simple enough conditions. however, proved under some stronger he tried weaken. In particular, [3] those were second order ones (expressible via formulas language spaces), attempts remedy simplify additional conditions needed resulted what presented monograph [4]. Recently another reached [11] [2], where last better diagonal recursive mappings. purpose establish general case, without any suppositions. method we use employed before author ([12], [14] others) outcome attempt reintroduce old technique coding Received January 15, 1999; revised August 16, 2000. * Supported part Contract No. 705/1998 Ministry Education Science Republic Bulgaria. ? 2001, Association Symbolic Logic 0022-48 12/01/6604-0013/$3.20