We presuppose the terminology of Moore [1]. In this paper, Moore proves that the existence of two mutually erasable configurations in a tessellation universe is a sufficient condition for the… Expand

There is a widespread current impression that the theory of Godel functionals, with quantifiers and choice, is the appropriate formalism for Bishop's book [1], but this is not so, and in more advanced mathematics the complexities become intolerable.Expand

It is shown that if T 1 is a finitely axiomatizable subtheory of T, there exists a consistent and decidable extension of T 1 which has the same constants as T 1 .Expand

The purpose of this paper is to prove two theorems and a conjecture (Conjecture II) announced in section 15 an earlier paper of the author's (cited as “ CT ”), and to compare them briefly with… Expand

Let us compare two properties of sets of non-negative integers: (1) the set a has property Γ, if there exists an effective procedure which when applied to any element of a different from its maximum… Expand

A system has the existence-property for abstracts (existence property for numbers, disjunction-property) if whenever F(3x)A(x), FA(t) for some abstract (t) (FA(n) for some numeral n; if whenever -A… Expand