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The converse of Moore’s Garden-of-Eden theorem
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
Constructive Set Theory
  • J. Myhill
  • Philosophy
    J. Symb. Log.
  • 1 September 1975
TLDR
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.
Choice Implies Excluded Middle
Solution of a Problem of Tarski
  • J. Myhill
  • Mathematics
    J. Symb. Log.
  • 1 March 1956
TLDR
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 .
Criteria of Constructibility for Real Numbers
  • J. Myhill
  • Mathematics
    J. Symb. Log.
  • 1 March 1953
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
Retraceable Sets
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
A Type-Free System Extending (ZFC)
A note on indicator-functions
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
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