منابع مشابه
Uniform Heyting arithmetic
We present an extension of Heyting Arithmetic in finite types called Uniform Heyting Arithmetic (HA) that allows for the extraction of optimized programs from constructive and classical proofs. The system HA has two sorts of first-order quantifiers: ordinary quantifiers governed by the usual rules, and uniform quantifiers subject to stronger variable conditions expressing roughly that the quant...
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Deduction Modulo is a formalism that aims at distinguish reasoning from computation in proofs. A theory modulo is formed with a set of axioms and a congruence de ned by rewrite rules: the reasoning part of the theory is given by the axioms, the computational part by the congruence. In deduction modulo, we can in particular build theories without any axiom, called purely computational theories. ...
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We apply to the semantics of Arithmetic the idea of “finite approximation” used to provide computational interpretations of Herbrand’s Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for ∨, ∃) over a suitable structure N for the language of natural numbers and maps of Gödel’s system T . We introduce a new Realizability semantics we call “Interactive le...
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In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like $S_{2}^i$ and $T_{2}^i$. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of p-cuts and small cuts. In particula...
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In 1983 Takeuchi showed that up to conjugation there are exactly 4 arithmetic subgroups of PSL2(R) with signature (1;∞). Shinichi Mochizuki gave a purely geometric characterization of the corresponding arithmetic (1;∞)-curves, which also arise naturally in the context of his recent work on inter-universal Teichmüller theory. Using Bely̆ı maps, we explicitly determine the canonical models of thes...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 1997
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2275651