Fine Structure is the name given to an analysis developed by Ronald Jensen in the late 60’s and early 70’s of Godel’s universe L of constructible sets with which Godel showed the consistency of the… Expand

We show that the halting times of innnite time Turing Machines (considered as or-dinals coded by sets of integers) are themselves all capable of being halting outputs of such machines. This gives a… Expand

It is argued that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate ‘is necessary’ can then be replaced by ‘ is necessarily true’.Expand

The extent to which semantic deficiency, stable truth, and nearly stable truth can be expressed in the object language is investigated and different axiomatic systems for the Revision Theory of Truth are studied.Expand

We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal… Expand

A hierarchy of strong axioms of infinity defined through normal filters, the α-weakly Erdős hierarchy, is defined, and it is shown that κ being α-Jonsson implies that it is α-Ramsey in the core model.Expand

The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a… Expand

Winning strategies for various Σ3-games in the L-hierarchy are located and the following are proved: there is a β-model of ∆ 1 3-CA0 + Σ 0 3Determinacy and the implication is not reversible.Expand