Recursive embeddings of partial orderings : (prepublication)
Krzysztof Rafal Apt · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1976
Let A be a countable atomless Boolean algebra and let X be a countable partial ordering.We prove that there exists an embedding of X into A which is recursive in X,A and which destroys all suprema and infima of X which can be destroyed.We show that the above theorem is false when we try to preserve all suprema and infima of X instead of destroying them.Finally we indicate that if A and Bare countable Boolean algebras and Bis atomless then A can be embedded into B by a function which is recursive in A,B.If A is also atomless, then there is an isomorphism from A into B which is recursive in A,B.