D. Scott. Completeness and axiomatiszability. Proceedings of the Tarski Symposium, pages 411--435, 1974. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On the Measure Problem - Coquand (2000) (Correct)
.... the measure problem Thierry Coquand Preliminary version at March 28, 2000 Abstract Using the notion of entailment relation [Sco74] we give a simple proof of a basic result of Tarksi (1929) on the existence of an additive function over a monoid. 1 Introduction There are several examples of topological spaces naturally associated to a mathematical structure: the spectrum (with Zariski topology) associated to a ring, the ....
D. Scott. Completeness and axiomatiszability. Proceedings of the Tarski Symposium, pages 411--435, 1974.
A Direct Proof of the Localic Hahn-Banach Theorem - Coquand (1999) (Correct)
.... Direct Proof of the Localic Hahn Banach Theorem Thierry Coquand Preliminary version at January 19, 1999 Abstract Using the notion of entailment relation [Sco74] we give a direct proof of the localic version of Hahn Banach s theorem. 1 Introduction There are several examples of topological spaces naturally associated to a mathematical structure: the spectrum (with Zariski topology) associated to a ring, the space of valuations associated to a field, ....
....[MP91] or in the work of Vermeulen [Ver86] but we think that our analysis is more perspicuous. In particular, a result of our analysis is a direct and elementary proof of the localic version of the Hahn Banach theorem. The key ingredient is the notion of entailment relation due to D. Scott [Sco74] which can be seen either as a way to generate a distributive lattice, or as an abstract generalisation of Gentzen multi conclusion sequent calculus. To any seminormed space E we associate such an entailment relation where the atomic propositions are pairs (x; r) where x 2 E and r 2 Q: Roughly ....
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D. Scott. Completeness and axiomatiszability. Proceedings of the Tarski Symposium, pages 411--435, 1974.
Real Spectrum - Coquand (1999) (Correct)
....m p = 0: We write A; B for A [ B and A; x for A [ fxg: Theorem 2. 1 The relation satisfies the following conditions of reflexivity, monotonicity and transitivity A B if A B 6= R) A B A; A 0 B; B 0 (M) A y; C A; y C A C (T ) Thus the relation is an entailment relation [Sco74]. 1 Proof. Only the rule (T ) is not direct. We show that if M is a multiplicative monoid and C a cone such that M C and x 2 A is such that we have some relations m 1 u 1 ( Gammax)v 1 = 0 m 2 x k u 2 xv 2 = 0 with m 1 ; m 2 2 M and u 1 ; v 1 ; u 2 ; v 2 2 P then there is a relation ....
D. Scott. Completeness and axiomatiszability. Proceedings of the Tarski Symposium, pages 411--435, 1974. 2
Valuations and Dedekind's Prague Theorem - Coquand, Persson (Correct)
.... Thierry Coquand and Henrik Persson Department of Computing Science, Chalmers University of Technology and University of Goteborg, SE 412 96 Goteborg, Sweden E mail: coquand cs.chalmers.se, henrikp cs.chalmers.se Abstract To any field K we associate an entailment relation in the sense of Scott [12]. In this way we can interpret an abstract propositional theory representing a generic valuation ring of a field, and obtain a simple effective proof of Dedekind s Prague theorem [5,6] Keywords: Valuations, Entailment relations. AMS class. 13A10, 13B25, 54H99 1 Introduction To any field K we ....
....of Dedekind s Prague theorem [5,6] Keywords: Valuations, Entailment relations. AMS class. 13A10, 13B25, 54H99 1 Introduction To any field K we associate a relation between finite sets of non zero elements of K which satisfy the three conditions of an entailment relation in the sense of Scott [12], and some further simple conditions. In this way, we can give constructive sense of a generic valuation ring of a field. Alternatively, this can be seen as a generalisation of the notion of integral element, and this notion can be used to prove that a given element is integral. As an example, we ....
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D. Scott. Completeness and axiomatiszability. Proceedings of the Tarski Symposium, pages 411--435, 1974. 10
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