Splitting theorems in recursion theory

Generalized splitting theorems

In (5), we and Fred Cohen gave some quite general splitting theorems. These described how to decompose the suspension spectra of certain filtered spaces CX as wedges of the suspension spectra of their successive filtration quotients Dq X. The spaces CX were of the form Cr x I r / ( ~ ) for suitable sequences of spaces {Cf} and {Xr}, and the construction CX was intended to be a reworking in 'pro...

Preservation theorems in {L}ukasiewicz \model theory

We present some model theoretic results for {L}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by Chang and Keisler.We prove compactness theorem with respect to the class of allstructures taking values in the {L}ukasiewicz $texttt{BL}$-algebra.We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemizatio...

Independence Results for n-Ary Recursion Theorems

The n-ary first and second recursion theorems formalize two distinct, yet similar, notions of self-reference. Roughly, the n-ary first recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n partial computable functions that use their own graphs in the manner prescribed by those tasks; the n-ary second recursion theorem says that, for any n algorithmic t...

A Classification of Viruses Through Recursion Theorems

We study computer virology from an abstract point of view. Viruses and worms are self-replicating programs, whose definitions are based on Kleene’s second recursion theorem. We introduce a notion of delayed recursion that we apply to both Kleene’s second recursion theorem and Smullyan’s double recursion theorem. This leads us to define four classes of viruses, two of them being polymorphic. The...

Ordinal Recursion Theory