Page 7 - Textos de Matemática Vol. 40
P. 7
Contents
Preface ................................... ix Introduction................................. 1
1 Applicative theories 7
1.1 Thelogicofpartialterms ...................... 7
1.1.1 Alanguageforapplicativetheories . . . . . . . . . . . . . 7
1.1.2 Thelogicalaxioms ...................... 9
1.1.3 Somecomments. ....................... 10
1.2 Combinatoryalgebra......................... 11 1.2.1 Firstresults. ......................... 12 1.2.2 Somecomments ....................... 14
1.3 ThetheoryBON ........................... 15 1.3.1 Theaxioms.......................... 15 1.3.2 Inductionprinciples ..................... 17 1.3.3 Primitiverecursion...................... 18 1.3.4 Someresultsandcomments................. 18
1.4 Models................................. 22 1.4.1 Recursiontheoreticmodels.................. 22 1.4.2 Termmodels ......................... 22
1.5 Prooftheory ............................. 24
1.5.1 Ordinalanalysis ....................... 25
1.5.2 Subsystemsofanalysis.................... 26
1.5.3 Theories of inductive definition and fixed point theories . 27
1.5.4 Kripke-Plateksettheory................... 29
1.6 Quantificationoperators....................... 30
1.6.1 The non-constructive μ and related operators . . . . . . . 30 1.6.2 TheSuslinoperator ..................... 32
1.7 N-strictness .............................. 32
1.7.1 Logical relations of the induction principles . . . . . . . . 33
1.7.2 TheaxiomofN-strictness .................. 33
1.7.3 Quantificationoperators................... 37
1.7.4 ThemissingN-strictnessinBON .............. 40
1.8 Acasestudy:leastfixedpoints................... 44 v
