论文信息 - The “world's simplest axiom of choice” fails - 字舞流文

The “world's simplest axiom of choice” fails

We use topos-theoretic methods to show that intuitionistic set theory with countable or dependent choice does not imply that every family, all of whose elements are doubletons and which has at most one element, has a choice function.

M. P. Fourman | A. Ščedrov | Michael P. Fourman | Andre Scedrov

[1] Michael P. Fourman,et al. Sheaf models for analysis , 1979 .

[2] Saul A. Kripke,et al. Semantical Analysis of Intuitionistic Logic I , 1965 .

[3] Ionel Bucur,et al. Toposes, Algebraic Geometry and Logic , 1972 .

[4] S. Maclane,et al. Categories for the Working Mathematician , 1971 .

[5] Michael P. Fourman,et al. Sheaf models for set theory , 1980 .

[6] Gerhard Osius,et al. Logical and set theoretical tools in elementary topoi , 1975 .

[7] M. Fourman. The Logic of Topoi , 1977 .

[8] Samuel Eilenberg,et al. Algebra, topology, and category theory : a collection of papers in honor of Samuel Eilenberg , 1976 .

[9] D. Scott,et al. Sheaves and logic , 1979 .

[10] Peter Freyd. The axiom of choice , 1980 .

[11] Saul A. Kripke,et al. Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[12] M. Makkai,et al. First order categorical logic , 1977 .