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French version |
The issues from 1 to 148 are also available on line at NUMDAM and at Revues.org for the following issues |
- Results for criterions:
- Topic: Sets
Results n° 1 to 8 of 15 matches
Page 1 . 2 . >> Next page
| Title | Type theory and proof processing system |
| Author | DOWEK Gilles |
| Keywords | Computation, Deduction, Function, Mathematical language, Proof, Proof processing systems, Set theory, Type theory |
| Topics | Computer Sciences, Computing, Logic, Sets, Software |
| Abstract | Since the end of the sixties, several computer programs allowing to process mathematical knowledge, and in particular mathematical proofs, have been designed. Building such programs raises new questions, in particular that of the conception of logical frameworks where mathematics can be formalized in practice. This is a new direction for fundational studies, more interested, so far, in formalization of mathematics in principle, than in practice. Several reasons explain that the designers of such programs often chose type theory rather than set theory to formalize mathematics. |
| Number | 165, Spring 2004, special issue: Constructive type theory |
| Language | French |
| Title | Proof Theory of Martin-Löf Type Theory. An overview |
| Author | SETZER Anton |
| Keywords | Generic programming, Inductive-recursive definitions, Kleene's O, Kripke Platek set theory, Mahlo universe, Martin-Löf type theory, Set theory, Well-founded trees |
| Topics | Logic, Orders and preorders, Sets, Trees, Type Theory |
| Abstract | We give an overview over the historic development of proof theory and the main techniques used in ordinal theoretic proof theory. We argue, that in a revised Hilbert's program, ordinal theoretic proof theory has to be supplemented by a second step, namely the development of strong equiconsistent constructive theories. Then we show, how, as part of such a programe, the proof theoretic analysis of Martin-Löf type theory with W-type and one microscopic universe containing only two finite sets is carried out. Then we look at the analysis Martin-Löf type theory with W-type and a universe closed under the W-type, and consider the extension of type theory by one Mahlo universe and its proof-theoretic analysis. Finally, we repeat the concept of inductive-recursive definitions, which extends the notion of inductive definitions substantially. We introduce a closed formalization, which can be used in generic programming, and explain, what is known about its strength. |
| Number | 165, Spring 2004, special issue: Constructive type theory |
| Language |  English |
| Title | The criticism of set theory in Brouwer's dissertation (1907) |
| Author | BOURDEAU Michel |
| Keywords | Continuum, Intuitionism, Ordinals, Transfinite |
| Topics | Epistemology, History of Mathematics, Logic, Orders and preorders, Sets |
| Abstract | Although Brouwer had not developed intuitionistic mathematics by 1917, some of his main ideas are already to be found in his 1907 Dissertation, for instance his attitude towards set theory. We are invited to distinguish two aspects in Cantor's creation: the authentic mathematical contribution (topology, ordinals), and a spurious one, which leads to contradictions and reflects an excessive confidence in the power of logic. Consequently, the transfinite has two faces: the hierarchy of the alephs, and the ordinals. Brouwer agrees with the latter, not with the former. This explains also why the Continuum Hypothesis is discussed in two different places: the mathematical version in the first chapter, the logical one in the third chapter. In the latter, Brouwer accepts the two generating principles for ordinals, but he thinks that these provide no ground for taking the second class of numbers as a completed totality. |
| Number | 164, Winter 2003 |
| Language | French |
| Title | Vicious circles, mathematics and logic |
| Author | LONGO Giuseppe |
| Keywords | Anti-foundation, Equation, Impredicativity, Self-application, Self-reference |
| Topics | Algebra, Epistemology, Logic, Orders and preorders, Sets, Type Theory |
| Abstract | Some forms of circularity in Logic and Mathematics (self-membership, self-application, impredicativity, .) are analyzed as closure properties of suitable mathematical structures since they can be considered as solutions of some systems of equations. At the same time, from a philosophical point of view, we stress the contribution of these circularities to the power of mathematics in making the world intelligible; |
| Number | 152, Winter 2000 |
| Language | French |
| Title | Set, measure and probability according to Borel |
| Author | CALLENS Stéphane |
| Keywords | None |
| Topics | History of Mathematics, Measure - Measurement, Probabilities, Sets |
| Abstract | |
| Number | 110, Summer 1990 |
| Language | French |
| Title | Meaningfulness and the Erlangen program of Felix Klein |
| Author | NARENS Louis E. |
| Keywords | None |
| Topics | Geometry, Measure - Measurement, Sets |
| Abstract | |
| Number | 101, Spring 1988, special issue: Measurement theory |
| Language | French |
| Title | Smullyan tables, Hintikka set and so on: algebraic point of view |
| Author | EYTAN Michel |
| Keywords | None |
| Topics | Algebra, Logic, Sets, Trees |
| Abstract | |
| Number | 48, Winter 1974 |
| Language | French |
| Title | About distances between sets of subsets |
| Author | BESSON Marie |
| Keywords | None |
| Topics | Correlation, Distances, Measure - Measurement, Sets |
| Abstract | |
| Number | 42, Summer 1973 |
| Language | French |
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