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Tripos theory in retrospect

ANDREW M. PITTS
2002 Mathematical Structures in Computer Science  
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

Andrew M. Pitts
1999 Electronical Notes in Theoretical Computer Science  
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 ...

Sloan Evans Despeaux
2009 Historia Mathematica  
[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  
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

Norbert Wiener
1949 Bulletin of the American Mathematical Society  
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

Lars Birkedal
2000 Electronical Notes in Theoretical Computer Science  
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  
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 [page]

1981 Mathematical Reviews  
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

Joan Richards
1988 Russell: the Journal of Bertrand Russell Studies  
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

Albert C Lewis
1990 Historia Mathematica  
, 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

JAUME NAVARRO
2010 British Journal for the History of Science  
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  
The sense of the meeting was opposed to a “triposin 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 ...

Patti W. Hunter
2007 Historia Mathematica  
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

J. D. Denton, J. P. Gostelow
2016 Biographical Memoirs of Fellows of the Royal Society  
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]

Étienne Miquey
2020 arXiv   pre-print
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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