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Indefinability in the
arithmetic isolic integers
Philip Olin |
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Vol. 29 (1969), No. 1, 175–186
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Abstract |
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This paper is primarily concerned with the theory of the arithmetic isolic integers. The following results are obtained: (1) No nonfinite member of the arithmetic isolic integers Λ∗(A) can be defined in Λ∗(A) even by an infinite number of arithmetic formulas (Theorem 4). (2) The arithmetic isols Λ(A) cannot be defined in Λ∗(A) even by an infinite number of arithmetic formulas (Theorem 7). (3) We exhibit some nonstandard models of arithmetic contained within Λ∗(A) (Theorem 10). The first result above follows from recent work of Nerode in the theory of isols, while the second strengthens his results to obtain the desired conclusion. |
Mathematical Subject Classification
Primary: 02.70
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Milestones
Received: 13 May 1968
Published: 1 April 1969
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Authors |
| Philip Olin | |
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