Internal and forcing models for the impredicative theory of classes

Rolando Chuaqui

GDML_Books, (1980), p.

Résumé

CONTENTSIntroduction............................................................................................................ 5I. Axiom system and elementary consequences........................................... 61. Axioms........................................................................................................................ 62. Definitions and elementary consequences........................................................ 9II. Principles of definitions by recursion........................................................... 123. Monotone operations.............................................................................................. 124. Recursion principles............................................................................................... 135. The rank function...................................................................................................... 15III. Well-ordering relations................................................................................... 166. Well-ordering relations............................................................................................ 197. Ordinals and -well-order types.............................................................................. 20IV. Models and satisfaction................................................................................. 258. Satisfaction................................................................................................................ 259. Absoluteness............................................................................................................ 2910. Models of MT........................................................................................................... 31V. The axiom of constructibility........................................................................... 3211. The axiom of constructibility................................................................................. 32VI. Ordined definability......................................................................................... 3712. Existence of hierarchies of all classes and relative constructibility............. 3713. Ordinal definability................................................................................................. 39VII. Complexity of the axiom system.................................................................. 4314. Non-finite axiomatizability and non-axiomatizability with sentences of bounded unrestricted quantifier depth.................. 4315. Complexity of axioms for the predicative sentences....................................... 46VIII. Forcing models............................................................................................. 4710. Forcing..................................................................................................................... 4717. Products of notions of forcing and coherent notions...................................... 55IX. Independence of axioms of choico.............................................................. 5918. Automorphisms of notions of forcing................................................................. 5919. Independence of the local axiom of choico....................................................... 6120. Independence of the global axiom of choico.................................................... 62References............................................................................................................ 65

Détail

Zbl 0458.03011

EUDML-ID : urn:eudml:doc:268378