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Tripos theory in retrospect
2002
Mathematical Structures in Computer Science
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The notion of tripos (Hyland, Johnstone, and Pitts 1980; Pitts 1981) was motivated by the desire to explain in what sense Higg's description of sheaf toposes as À-valued sets and Hyland's realizability ...
Triposes satisfy this property, but there are examples of non-triposes satisfying this form of comprehension. ...
In particular, (Pitts 1981) establishes quite a rich theory of triposes akin to that for sheaf theory, involving notions of geometric morphism, Lawvere-Tierney topologies, etc. ...
doi:10.1017/s096012950200364x
fatcat:nsa5kpggojbyzee4hh7qw7dv6u
Tripos Theory in Retrospect
1999
Electronical Notes in Theoretical Computer Science
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Pitts generic predicate of the tripos (Theorem 4.4). ...
We s a w in Example 4.8 that hyperdoctrines satisfying (CA) do not necessarily have generic predicates, so the notion of brewise quanti cation and its consequences for iteration are not so useful in that ...
theory of triposes over an arbitrary base. ...
doi:10.1016/s1571-0661(04)00107-0
fatcat:3ezdcaxze5ak3g5l6fnqk3k7ny
Review††Edited by Adrian Rice and Antoni MaletAll books, monographs, journal articles, and other publications (including films and other multisensory materials) relating to the history of mathematics are abstracted in the Abstracts Department. The Reviews Department prints extended reviews of selected publications.Materials for review, except books, should be sent to the Abstracts Editor, Sloan Despeaux, Western Carolina University, Cullowhee, NC 28723, USA. Books in English for review should be sent to Adr
...
2009
Historia Mathematica
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[Several questions from the Tripos and analysis of student solutions can be found in Andrew Warwick's Masters of Theory (Warwick, 2003, e.g. 18-24 and 163-167) , and June Barrow-Green's excellent discussion ...
The university owed much of its preeminence in the field to its mathematical Tripos examination. ...
doi:10.1016/j.hm.2008.08.006
fatcat:75jotj5c2vcjhku2f3fpjx2w7a
Page 4913 of Mathematical Reviews Vol. , Issue 2003g
[page]
2003
Mathematical Reviews
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Pym (Bath)
2003¢:03110 03G30 18C10 68Q55
Pitts, Andrew M. (4-CAMB-C; Cambridge)
Tripos theory in retrospect. (English summary)
Realizability (Trento, 1999).
Math. Structures Comput. ...
Here it is proven that, starting from a tripos, the related hyperdoctrine satisfies a comprehension property such that the resulting logos is actually a topos. ...
Godfrey Harold Hardy 1877-1947
1949
Bulletin of the American Mathematical Society
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in the Tripos, has not been published since 1912. ...
participated in it, and their subsequent activity became retrospective rather than creative. ...
doi:10.1090/s0002-9904-1949-09165-6
fatcat:vrknkbq5v5atdo3nuazj44jw5e
Developing Theories of Types and Computability via Realizability
2000
Electronical Notes in Theoretical Computer Science
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We i n vestigate the development of theories of types and computability via realizability. ...
He has taught me most of the topos theory I know and our collaboration has been very fruitful, I think. ...
The notion of tripos was invented by Hyland, Johnstone and Pitts HJP80 and the theory of triposes over general base categories was developed by Pitts in his Ph.D.thesis Pit81 ; see also Pit99 for a retrospective ...
doi:10.1016/s1571-0661(05)80642-5
fatcat:mcnve2jp4nc47or7jvohayeni4
Obituary Notices
1930
Proceedings of the Royal Society A
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And it was in this subject of elliptic functions that he specialised, particularly in the Jacobi theory. ...
in the general theory of functions, associated with the names of Cauchy, Weierstrass and Riemann. ...
After having been Instructor in Chemistry at the Royal School of Naval Architecture he was appointed in 1870 Demonstrator in Chemistry at Cambridge. ...
doi:10.1098/rspa.1930.0024
fatcat:lqgzqswlgrgfrpxmrauf67kxqm
Page 1627 of Mathematical Reviews Vol. , Issue 81E
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1981
Mathematical Reviews
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spite of the fact that in retrospect he does not appear to have been the greater mathematician. ...
and his famous “The case against the mathematical tripos”), the 1928 Rouse Ball lecture (“Mathe- matical proof”), “Mathematics” in Oxford Magazine (his plea for a Mathematical Institute was granted 23 ...
Bertrand Russell's Essay on the Foundations of Geometry and the Cambridge Mathematical Tradition
1988
Russell: the Journal of Bertrand Russell Studies
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THE BRITISH MATHEMATICAL TRADITION In his retrospective writings, Russell consistently criticized the mathematical education he had received at Cambridge in the 1890's. ...
Their central role in Cayley's projective theory of distance served merely to emphasize to him the irrelevance of that theory to the essential spatial concept. ...
doi:10.15173/russell.v8i1.1733
fatcat:j2hmmd6mazfgdiar3mbhxsgmse
Mathematical visions: The pursuit of geometry in victorian England
1990
Historia Mathematica
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, is largely gleaned from retrospective treatments by those who lived through this period. ...
the restructuring of the tripos from year to year. ...
doi:10.1016/0315-0860(90)90015-6
fatcat:3xr7cx6qwrcffc53s4x3pcvzti
Electron diffraction chez Thomson: early responses to quantum physics in Britain
2010
British Journal for the History of Science
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Both Thomsons were trained in the pedagogical tradition of classical physics in the Cambridge Mathematical Tripos, and this certainly influenced their understanding of quantum physics and early quantum ...
of the new quantum mechanics in the latter. ...
Tripos in 1867, C. ...
doi:10.1017/s0007087410000026
fatcat:qgcw63w4nfbrjdbktulajg5p5i
Page 600 of The Athenaeum Vol. , Issue 3211
[page]
1889
The Athenaeum
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The sense of the meeting was opposed to a “tripos ” in the strict sense of the word, but in favour of the recog- nition by the universities both of the theory and practice of teaching. Mr. ...
In conclusion we may note an interesting debate on ‘A Teachers’ Tripos,’ introduced by Prof. ...
Review††Edited by Adrian Rice and Antoni MaletAll books, monographs, journal articles, and other publications (including films and other multisensory materials) relating to the history of mathematics are abstracted in the Abstracts Department. The Reviews Department prints extended reviews of selected publications.Materials for review, except books, should be sent to the Abstracts Editor, Sloan Despeaux, Western Carolina University, Cullowhee, NC 28723, USA. Books in English for review should be sent to Adr
...
2007
Historia Mathematica
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mathematical Tripos of the late 19th century. ...
As with his earlier work on choice theory, the project fell upon deaf ears. ...
David Pengelley begins the work by giving us some brief selections from Arthur Cayley's first paper on group theory [Cayley, 1854] and then showing how to make use of these excerpts in an introductory ...
doi:10.1016/j.hm.2006.07.003
fatcat:qj32dvel6fdjngedey2g2tsbwq
Sir John Harold Horlock FREng. 19 April 1928 — 22 May 2015
2016
Biographical Memoirs of Fellows of the Royal Society
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In the third year he studied for Part II of the Tripos. ...
In retrospect it is surprising that such a complex laboratory could have been constructed so quickly and at such a modest cost. ...
Bibliography The following publications are those referred to directly in the text. ...
doi:10.1098/rsbm.2016.0009
fatcat:vqpgl5rxbjfdlb5n4lifng65ye
Revisiting the duality of computation: an algebraic analysis of classical realizability models
[article]
2020
arXiv
pre-print
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In particular, he proved that classical realizability subsumes Cohen's forcing, and even more, gives rise to unexpected models of set theories. ...
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. ...
Acknowledgment The author would like to thank Alexandre Miquel to which several ideas in this paper, especially the definition of conjunctive separators, should be credited. ...
arXiv:1910.02732v2
fatcat:s7lsy6kuvjekrfwnbwk2355era
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