Abstract. We prove new upper bound theorems on the consistency strengths of SPFA(), SPFA(-linked) and SPFA(+ -cc). Our results are in terms of (, )-subcompactness, which is a new l...
free but not Whitehead Abelian groups to construct Abstract Elementary Classes (AEC) which satisfy the amalgamation property but fail various conditions on the locality of Galois-...
When restricted to proving q i formulas, the quantified propositional proof system G i is closely related to the b i theorems of Buss's theory Si 2. Namely, G i has polynomial...
An important technique in large cardinal set theory is that of extending an elementary embedding j : M N between inner models to an elementary embedding j : M[G] N[G] between ge...
We investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite B...
We say that A LR B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real , oracle B can also find patterns on . In o...
George Barmpalias, Andrew E. M. Lewis, Mariya Ivan...