If the initial segment Σ of Ω is a set, then it has a least strict upper bound S(Σ) ∈ Ω. Thus, for numbers α = S(Σ) and β = S(Σ′), α < β iff α ∈ Σ′; α = β iff Σ = Σ′; S(∅) is the least number 0… (More)

The volumes of Gödel’s collected papers under review consist almost entirely of a rich selection of his philosophical/scientific correspondence, including English translations face-to-face with the… (More)

Kurt Gödel: Collected Works Volume III [Gödel, 1995] contains a selection from Gödel’s Nachlass; it consists of texts of lectures, notes for lectures and manuscripts of papers that for one reason or… (More)

The background of these remarks is that in 1967, in ‘’Constructive reasoning” [27], I sketched an argument that finitist arithmetic coincides with primitive recursive arithmetic, PRA; and in 1981, in… (More)

I will be discussing the axiomatic conception of mathematics, the modern version of which is clearly due to Hilbert; but one aspect of it goes back to Cantor. I refer here to Hilbert’s view that the… (More)

Restricted to first-order formulas, the rules of inference in the Curry-Howard type theory are equivalent to those of first-order predicate logic as formalized by Heyting, with one exception:… (More)