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| -rw-r--r-- | theories/Logic/Diaconescu.v | 20 |
1 files changed, 10 insertions, 10 deletions
diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v index 23af5afc6..896be7c33 100644 --- a/theories/Logic/Diaconescu.v +++ b/theories/Logic/Diaconescu.v @@ -8,9 +8,9 @@ (************************************************************************) (** Diaconescu showed that the Axiom of Choice entails Excluded-Middle - in topoi [Diaconescu75]. Lacas and Werner adapted the proof to show + in topoi [[Diaconescu75]]. Lacas and Werner adapted the proof to show that the axiom of choice in equivalence classes entails - Excluded-Middle in Type Theory [LacasWerner99]. + Excluded-Middle in Type Theory [[LacasWerner99]]. Three variants of Diaconescu's result in type theory are shown below. @@ -23,22 +23,22 @@ Benjamin Werner) C. A proof that extensional Hilbert epsilon's description operator - entails excluded-middle (taken from Bell [Bell93]) + entails excluded-middle (taken from Bell [[Bell93]]) - See also [Carlström] for a discussion of the connection between the + See also [[Carlström04]] for a discussion of the connection between the Extensional Axiom of Choice and Excluded-Middle - [Diaconescu75] Radu Diaconescu, Axiom of Choice and Complementation, + [[Diaconescu75]] Radu Diaconescu, Axiom of Choice and Complementation, in Proceedings of AMS, vol 51, pp 176-178, 1975. - [LacasWerner99] Samuel Lacas, Benjamin Werner, Which Choices imply + [[LacasWerner99]] Samuel Lacas, Benjamin Werner, Which Choices imply the excluded middle?, preprint, 1999. - [Bell93] John L. Bell, Hilbert's epsilon operator and classical + [[Bell93]] John L. Bell, Hilbert's epsilon operator and classical logic, Journal of Philosophical Logic, 22: 1-18, 1993 - [Carlström04] Jesper Carlström, EM + Ext_ + AC_int <-> AC_ext, - Mathematical Logic Quaterly, vol 50(3), pp 236-240, 2004. + [[Carlström04]] Jesper Carlström, EM + Ext_ + AC_int is equivalent + to AC_ext, Mathematical Logic Quaterly, vol 50(3), pp 236-240, 2004. *) (**********************************************************************) @@ -263,7 +263,7 @@ End ProofIrrel_RelChoice_imp_EqEM. (**********************************************************************) (** * Extensional Hilbert's epsilon description operator -> Excluded-Middle *) -(** Proof sketch from Bell [Bell93] (with thanks to P. Castéran) *) +(** Proof sketch from Bell [[Bell93]] (with thanks to P. Castéran) *) Local Notation inhabited A := A (only parsing). |