A. Kock Universal projective geometry via topos theory. J. Pure Appl. Algebra 9 (1976/77), no. 1, 1-24. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Classifying Toposes for First Order Theories - Butz, Johnstone (1997) (1 citation) (Correct)
....one to one. However, although a very large proportion of the first order theories encountered in mathematical practice are (at least Morita equivalent to) geometric ones, we do occasionally need to consider models of theories which are not geometric. For example, as was first observed by Kock [14], it can often be profitable to consider the non geometric first order sentences satisfied by the generic model of a geometric theory. For such theories, we cannot hope to have a classifying topos in the above sense, since it is well known that geometric theories are exactly those whose models ....
....easily that B (T) exists and) coincides with (T) Conversely, if a geometric theory T is equivalent to its geometrically saturated extension T, as defined in 4.3, then every geometric morphism into (T) is open, and so the latter must be Boolean. Thus the phenomenon first observed by Kock [14], that the generic model of a geometric theory may satisfy first order sentences not derivable from that theory, is typical of all such theories having non Boolean classifying toposes. We recall that in [1] Blass and Scedrov characterized those coherent (that is, geometric) theories whose ....
A. Kock: Universal projective geometry via topos theory, J. Pure Appl. Alg. 9 (1976), 1--24. 33
Classifying Toposes for First Order Theories - Butz, Johnstone (1998) (1 citation) (Correct)
....one to one. However, although a very large proportion of the first order theories encountered in mathematical practice are (at least Morita equivalent to) geometric ones, we do occasionally need to consider models of theories which are not geometric. For example, as was first observed by Kock [14], it can often be profitable to consider the non geometric first order sentences satisfied by the generic model of a geometric theory. For such theories, we cannot hope to have a classifying topos in the above sense, since it is wellknown that geometric theories are exactly those whose models are ....
....B fo (T) exists and) coincides with B g (T) Conversely, if a geometric theory T is equivalent to its geometrically saturated extension T, as defined in 4.3, then every geometric morphism into B g (T) is open, and so the latter must be Boolean. Thus the phenomenon first observed by Kock [14], that the generic model of a geometric theory may satisfy first order sentences not derivable from that theory, is typical of all such theories having non Boolean classifying toposes. We recall that in [1] Blass and Scedrov characterized those coherent (that is, geometric) theories whose ....
A. Kock: Universal projective geometry via topos theory, J. Pure Appl. Alg. 9 (1976), 1--24.
Classifying Toposes for First Order Theories - Butz, Johnstone (1997) (1 citation) (Correct)
....one to one. However, although a very large proportion of the rst order theories encountered in mathematical practice are (at least Morita equivalent to) geometric ones, we do occasionally need to consider models of theories which are not geometric. For example, as was rst observed by Kock [14], it can often be pro table to consider the non geometric rst order sentences satis ed by the generic model of a geometric theory. For such theories, we cannot hope to have a classifying topos in the above sense, since it is well known that geometric theories are exactly those whose models are ....
....that B fo (T) exists and) coincides with B g (T) Conversely, if a geometric theory T is equivalent to its geometrically saturated extension T, as de ned in 4.3, then every geometric morphism into B g (T) is open, and so the latter must be Boolean. Thus the phenomenon rst observed by Kock [14], that the generic model of a geometric theory may satisfy rst order sentences not derivable from that theory, is typical of all such theories having non Boolean classifying toposes. We recall that in [1] Blass and Scedrov characterized those coherent (that is, geometric) theories whose ....
A. Kock: Universal projective geometry via topos theory, J. Pure Appl. Alg. 9 (1976), 1-24. 33
A Sheaf-Theoretic Reformulation Of The Tate Conjecture - Kahn (1997) (2 citations) (Correct)
....: x r g be a finite set of points of X and Y = Spec OX;x1 ; x r . Then the Gersten complex 0 H i cont (Y=k; Z l (n) a y2Y (0) H i cont (k(y) k; Z l (n) a y2Y (1) H i Gamma1 cont (k(y) k; Z l (n Gamma 1) is universally exact in the sense of Grayson [13] for all i. If X 0 f Gamma X is finite and flat, the diagram 0 H i cont (Y 0 =k; Z l (n) a y2Y 0 (0) H i cont (k(y) k; Z l (n) a y2Y 0 (1) H i Gamma1 cont (k(y) k; Z l (n Gamma 1) f y f y f y 0 H i cont (Y=k; Z l (n) a y2Y (0) ....
D. Grayson Universal exactness in algebraic K-theory, J. Pure Appl. Algebra 36 (1985), 139--141.
A Completness Proof for Geometrical Logic - Coquand (Correct)
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A. Kock Universal projective geometry via topos theory. J. Pure Appl. Algebra 9 (1976/77), no. 1, 1-24.
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