A combinatorial analysis of functions provably recursive in
A definition of exponentiation by a bounded arithmetical formula
A direct proof of Gödel's incompleteness theorem.
A further restricted ω-rule
A Godel-Functional Interpretation of the ω-Rule
A logical analysis of the truth-reaction paradox
A nonstandard approach to arithmetic.
A note of definable skolem functions
A note on a proof of Sherpherdson.
A note on a result of Buss concerning bounded theories and the collection scheme.
A note on bounded arithmetic
A note on proofs of falsehood.
A note on the Mac Dowell-Specker theorem
A note on Δ₁ induction and Σ₁ collection
Slaman recently proved that Σₙ collection is provable from Δₙ induction plus exponentiation, partially answering a question of Paris. We give a new version of this proof for the case n = 1, which only requires the following very weak form of exponentiation: " exists for some y sufficiently large that x is smaller than some primitive recursive function of y".
A recursion-theoretic characterization of instances of provable in
A sequence of theories for arithmetic whose union is complete
A simple detailed proof for Goedel's incompleteness theorem
Addendum to “A note on the MacDowell–Specker theorem”
An application of a reflection principle
We define a recursive theory which axiomatizes a class of models of IΔ₀ + Ω ₃ + ¬ exp all of which share two features: firstly, the set of Δ₀ definable elements of the model is majorized by the set of elements definable by Δ₀ formulae of fixed complexity; secondly, Σ₁ truth about the model is recursively reducible to the set of true Σ₁ formulae of fixed complexity.
An interpretation of in -NIA.