منابع مشابه
Nonstandard arithmetic and reverse mathematics
We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [HKK1984] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles ...
متن کاملNonstandard arithmetic and recursive comprehension
First order reasoning about hyperintegers can prove things about sets of integers. In the author’s paper Nonstandard Arithmetic and Reverse Mathematics, Bulletin of Symbolic Logic 12 (2006), it was shown that each of the “big five” theories in reverse mathematics, including the base theory RCA0, has a natural nonstandard counterpart. But the counterpart RCA0 of RCA0 has a defect: it does not im...
متن کاملArithmetic Nullstellensatz and Nonstandard Methods
In this study we find height bounds for polynomial rings over integral domains. We apply nonstandard methods and hence our constants will be ineffective. Furthermore we consider unique factorization domains and possible bounds for valuation rings and arithmetical functions.
متن کاملWeak Theories of Nonstandard Arithmetic and Analysis
A general method of interpreting weak higher-type theories of nonstandard arithmetic in their standard counterparts is presented. In particular, this provides natural nonstandard conservative extensions of primitive recursive arithmetic, elementary recursive arithmetic, and polynomial-time computable arithmetic. A means of formalizing basic real analysis in such theories is sketched. §
متن کاملTransfer principles in nonstandard intuitionistic arithmetic
Using a slight generalization, due to Palmgren, of sheaf semantics, we present a term-model construction that assigns a model to any first-order intuitionistic theory. A modification of this construction then assigns a nonstandard model to any theory of arithmetic, enabling us to reproduce conservation results of Moerdijk and Palmgren for nonstandard Heyting arithmetic. Internalizing the constr...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1967
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1967-11809-3