• Publications
  • Influence
Σ * Fine Structure
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
The Length of Infinite Time Turing Machine Computations
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
Necessities and Necessary Truths: A Prolegomenon to the Use of Modal Logic in the Analysis of Intensional Notions
TLDR
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’.
Coding the Universe
REVISION REVISITED
TLDR
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.
On the Possibility, or Otherwise, of Hypercomputation
  • P. Welch
  • Mathematics
    The British Journal for the Philosophy of Science
  • 1 December 2004
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
Greatly Erdős cardinals with some generalizations to the Chang and Ramsey properties
TLDR
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.
Gödel's Disjunction: The scope and limits of mathematical knowledge
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
Weak systems of determinacy and arithmetical quasi-inductive definitions
  • P. Welch
  • Mathematics, Computer Science
    J. Symb. Log.
  • 26 May 2009
TLDR
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.
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