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Fourman, M. P.; Ščedrov, A.

The ”World’s simplest axiom of choice” fails. (English) Zbl 0499.03048

Manuscr. Math. 38, 325-332 (1982).
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Cited in 5 Documents

MSC:

03G30 Categorical logic, topoi
03F50 Metamathematics of constructive systems
03E25 Axiom of choice and related propositions
18B25 Topoi

Keywords:

intuitionistic set theory with countable or dependent choice; field extension; choice of roots; generic model; choice function; forcing over categories; intuitionistic ZF; presheaf topos

Software:

KRIPKE
Cite Review PDF
Full Text: DOI EuDML

References:

[1] DUMMETT, M.A.E.: Elements of Intuitionism. Oxford University Press, Oxford (1977) · Zbl 0358.02032
[2] FOURMAN, M.P.: The logic of topoi. In: Handbook of Mathematical Logic (ed. J. Barwise), North Holland, Amsterdam (1977), 1053–1090
[3] FOURMAN, M.P.: Sheaf models for set theory. J. Pure and Applied Algebra 19 (1980), 91–101 · Zbl 0446.03041 · doi:10.1016/0022-4049(80)90096-1
[4] FOURMAN, M.P. and GRAYSON, R.J.: Formal spaces induction principles and completeness theorems. In preparation · Zbl 0537.03040
[5] FOURMAN, M.P. and HYLAND, J.M.E.: Sheaf models for analysis. In: Applications of Sheaves (Proc. L.M.S. Durham Symposium, 1977), Springer Lecture Notes in Math. 753 (1979) · Zbl 0427.03028
[6] FOURMAN, M.P. and SCOTT, D.S.: Sheaves and logic. In: Applications of Sheaves (Proc. L.M.S. Durham Symposium, 1977), Springer Lecture Notes in Math. 753 (1979) · Zbl 0415.03053
[7] FREYD, P.: The axiom of choice. J. Pure and Applied Algebra 19 (1981), 103–125 · Zbl 0446.03042 · doi:10.1016/0022-4049(80)90097-3
[8] JOYAL, A. and REYES, G.: Generic models in categorical logic. J. Pure and Applied Algebra (to appear)
[9] KRIPKE, S.: Semantical analysis of intuitionistic logic I. Z. math. logik u Grundl. Math. 9 (1963), 67–96 · Zbl 0118.01305 · doi:10.1002/malq.19630090502
[10] LAWVERE, F.W.: Introduction. In: Toposes, Algebraic Geometry and Logic. Springer Lecture Notes in Math. 274 (1972), 1–12 · doi:10.1007/BFb0073962
[11] MACLANE, S.: Categories for the Working Mathematician. Springer-Verlag, Heidelberg · Zbl 0705.18001
[12] MAKKAI, M. and REYES, G.: First-order categorical logic. Springer Lecture Notes in Math. 611 (1977) · Zbl 0357.18002
[13] OSIUS, G.: Logical and Set-Theoretical Tools in Elementary Topoi. In: Model Theory and Topoi. Springer Lecture Notes in Math. 445 (1975), 297–346 · Zbl 0348.18002 · doi:10.1007/BFb0061299
[14] ŠČEDROV, A.: Consistency and Independence Proofs in intuitionistic set theory. Proceedings of the New Mexico Conference on Constructive Mathematics (F. Richman, ed.), Springer Lecture Notes (to appear)
[15] SCOTT, D.S.: Sheaf models for set theory. To appear
[16] TIERNEY, M.: Forcing Topologies and Classifying Topoi, in Algebra, Topology and Category Theory; a collection of papers in honor of Samuel Eilenberg (A. Heller, ed.), Academic Press, New York (1976), 211–219
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