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An axiomatic approach to algebrization

2009
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Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09
*

In this paper, building on the work of Arora, Impagliazzo, and Vazirani [4], we propose

doi:10.1145/1536414.1536509
dblp:conf/stoc/ImpagliazzoKK09
fatcat:o6tthbtumnde3criihmkxnzxbm
*an**axiomatic**approach**to*"*algebrization*", which complements and clarifies the*approaches*of [12] and [1]. ...*to*one oracle*to*classes relative*to**an*algebraic extension of that oracle. ... We want*to*thank Scott Aaronson, Lance Fortnow, and the anonymous referees for their comments. ...##
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Page 924 of Mathematical Reviews Vol. 37, Issue 4
[page]

1969
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Mathematical Reviews
*

Ludwig, Giinther 5003 Attempt of

*an**axiomatic*foundation of quantum mechanics and more general theories. II. Comm. Math. Phys. 4 (1967), 331-348. ... Jauch (Geneva) Ludwig, Giinther 5004 Attempt of*an**axiomatic*foundation of quantum mechanics and more general theories. III. Comm. Math. Phys. 9 (1968), 1-12. ...##
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Page 516 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 56, Issue 6
[page]

1950
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American Mathematical Society. Bulletin of the American Mathematical Society
*

Steenrod,

*Axiomatic**approach**to*homology theory, Proc. Nat. Acad. Sci. U. S. A. vol. 31 (1945) pp. 117-120. 10. , Foundations of algebraic topology,*to*appear. 11. K. ... 516 SAUNDERS MacLANE tions between vector spaces) can be deduced from our self-dual sys- tem of axioms for*an*abelian bicategory. ...##
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Page 3145 of Mathematical Reviews Vol. , Issue 2004d
[page]

2004
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Mathematical Reviews
*

From the introduction: “The purpose of the present note is

*to*show how the*axiomatic**approach**to*Tate cohomology of J. Greenlees [J. Pure Appl. ... In*an*erratum [*Algebr*. Geom. Topol., submitted] the author has corrected several mistakes and misleading statements. ...##
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Page 9337 of Mathematical Reviews Vol. , Issue 2002M
[page]

2002
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Mathematical Reviews
*

The author advocates

*an*innovative*approach**to*quantized gauge theories using mathematically well-defined ob- jects developed within the framework of*axiomatic*quantum field theory and causal perturbation ... Within this*approach*all couplings are determined by perturbative gauge invariance without the use of spontaneous symmetry breaking. As*an*application the elec- troweak theory is constructed. ...##
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Page 4969 of Mathematical Reviews Vol. , Issue 84m
[page]

1984
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Mathematical Reviews
*

Then a unifying

*approach*for the Brelot and Hervé decomposition is presented. ... Finally*an*abstract decomposition result is proved within the framework of potential cones showing the validity of Brelot’s decomposition in more general*axiomatics*. ...##
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Algèbre noethérienne non commutative, by L. Lesieur et R. Croisot. [Mém. Sci. Math. 154] Gauthier-Villars, Paris 1963. 117 pages

1964
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Canadian mathematical bulletin
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One of the reasons for the reluctance of senior faculty members

doi:10.1017/s0008439500031957
fatcat:mm5ejwgjobbufcvbvulecypt2q
*to*teach the course is the lack of discipline and organization in the standard textbook. ... Any mathematician will find it a genuine pleasure*to*teach from this reprinting of Professor Albert 1 s book. In the preface the author states: "College Algebra has a basic unity. ...*To*achieve this object, he*approaches*the subject from a semi-*axiomatic*point of view and uses a style which is always explicit rather than concise. ...##
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Page 1300 of Mathematical Reviews Vol. , Issue 80D
[page]

1980
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Mathematical Reviews
*

The author gives

*an**axiomatization*of Birkhoff and von Neumann’s quantum logic extended by the definition of the func- tor —,, i=0,1,2,3,4,*an**axiomatization*of E(M.,, ;) and axiomatiza- tions of E(M,, ... This paper contains a short elementary introduction*to*nonstan- dard analysis very similar*to*the classical*approach*based on ultra- powers. ...##
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Page 7720 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
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Mathematical Reviews
*

Level 0 of such

*an**axiomatization*consists in requiring the tensor product*to*be exact in each variable. This is what everybody agrees about and this is already a workable framework. ... (English summary)*Algebr*. Represent. Theory 6 (2003), no. 5, 475-499. ...##
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Page 1807 of Mathematical Reviews Vol. 50, Issue 6
[page]

1975
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Mathematical Reviews
*

The author chooses

*an**axiomatic**approach**to*category theory without using any set theory: the usual axioms describing the inner structures of categories, the axioms for functors together with the axiom ... In addition*to*the articles cited above a similar point of view was expressed in*an*article by M. F. Atiyah [Bild Wissensch. 6 (1969), 314-323]. J. S. Joel (Ann Arbor, Mich.) ...##
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Page 580 of Mathematical Reviews Vol. 50, Issue 3
[page]

1975
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Mathematical Reviews
*

When it first appeared it was one of the few books that presented a modern

*approach**to*mathematics (including*an**axiomatic**approach**to*algebra) at a really elementary level and with the clarity that that ... E. 4176 ntroduction a |’*algébre*moderne. ...##
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Les fondements de la géométrie. Tome II: Géométrie projective par Bêla Kerékjarto. Gauthier-Villars, Paris, et Académie des Sciences hongroise, 1966. 528 pages. $14.50

1968
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Canadian mathematical bulletin
*

élémentaire", Paris, Hermann 1964, as well as

doi:10.1017/s0008439500028988
fatcat:2atswe5azrcojl53ms7r2ryo4i
*to*the more recently developed*approaches**to*euclidean geometry (cf. e.g. ... Today, however, when everywhere less and less attention is given*to*Hilbert's*axiomatical*scheme,*an*exposition of projective geometry on this basis will hardly carry along the imagination of young geometers ...##
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Page 3542 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
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Mathematical Reviews
*

It presents

*an*interesting discussion on the*axiomatization*of quantum mechanics. ... Differ- ent*approaches*are compared, in particular, the traditional setting where observables are represented by selfadjoint operators on a Hilbert space and the*axiomatization*where observables are rep ...##
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Page 3271 of Mathematical Reviews Vol. , Issue 85h
[page]

1985
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Mathematical Reviews
*

His semantic

*approach*led*to*the universal algebraic concept of a relation algebra. ...*to**an*operation free sentence in at most three variables. ...##
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Page 2007 of Mathematical Reviews Vol. 56, Issue 6
[page]

1978
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Mathematical Reviews
*

The author treats in a very elementary way sore of the ideas
that have been used in the development of

*approaches**to*Hilbert’s first problem: the use of model theory and the work of P. J. ... The article ends with*an*interpretation of what it would mean for X-automata*to*have C above as a groupoid, i.e.,*to*have Booleanness, hence classical logic. ...
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