منابع مشابه
Constraint Satisfaction Problems around Skolem Arithmetic
We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glaßer et al. [17] in the context of CSPs and settle the major open question from that paper, finding a certain satisfaction problem on circuits to be decidable. This we prove using the decidability of Skolem Arithmetic. We continue by studying first-order expans...
متن کاملInteractive Realizability for Classical Peano Arithmetic with Skolem Axioms
Interactive realizability is a computational semantics of classical Arithmetic. It is based on interactive learning and was originally designed to interpret excluded middle and Skolem axioms for simple existential formulas. A realizer represents a proof/construction depending on some state, which is an approximation of some Skolem functions. The realizer interacts with the environment, which ma...
متن کاملEliminating Skolem Functions in Peano Arithmetic with Interactive Realizability
We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result – which shows that the Excluded Middle principle can be used to eliminate Skolem functions – has been previously proved by other techniques, among them the epsilon substitution method and forcing. In our proof, we employ Inter...
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 کاملRecursive Double-Size Fixed Precision Arithmetic
We propose a new fixed precision arithmetic package called RecInt. It uses a recursive double-size data-structure. Contrary to arbitrary precision packages like GMP, that create vectors of words on the heap, RecInt large integers are created on the stack. The space allocated for these integers is a power of two and arithmetic is performed modulo that power. Operations are thus easily implemente...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1962
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10647