Collapsing degrees

Collapsing Polynomial-Time Degrees

For reducibilities r and r′ such that r is weaker than r′, we say that the r-degree of A, i.e., the class of sets which are r-equivalent to A, collapses to the r′-degree of A if both degrees coincide. We investigate for the polynomial-time bounded many-one, bounded truth-table, truth-table, and Turing reducibilities whether and under which conditions such collapses can occur. While we show that...

Collapsing Degrees via Strong Computation

Though Berman and others have provided powerful techniques to collapse nondeterministic degrees at and above nondeterministic linear space, and Immerman and Szelepcsenyi have provided techniques that collapse even sublinear nondeterministic space classes, it has remained an open problem whether any collapses could be proven for sublinear nondeterministic space degrees. This paper provides the f...

Collapsing Closures

A description in the Jacobs and Langen domain is a set of sharing groups where each sharing group is a set of program variables. The presence of a sharing group in a description indicates that all the variables in the group can be bound to terms that contain a common variable. The expressiveness of the domain, alas, is compromised by its intractability. Not only are descriptions potentially exp...

Collapsing functions

We define what it means for a function on ω1 to be a collapsing function for λ and show that if there exists a collapsing function for (21), then there is no precipitous ideal on ω1. We show that a collapsing function for ω2 can be added by forcing. We define what it means to be a weakly ω1-Erdös cardinal and show that in L[E], there is a collapsing function for λ iff λ is less than the least w...

On Collapsing Narrowing