Internal and forcing models for the impredicative theory of classes

Rolando Chuaqui

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1980

Abstract

top
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

How to cite

top

Rolando Chuaqui. Internal and forcing models for the impredicative theory of classes. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1980. <http://eudml.org/doc/268378>.

@book{RolandoChuaqui1980,
abstract = {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},
author = {Rolando Chuaqui},
keywords = {well-orderings; inductive constructions; axiomatization},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Internal and forcing models for the impredicative theory of classes},
url = {http://eudml.org/doc/268378},
year = {1980},
}

TY - BOOK
AU - Rolando Chuaqui
TI - Internal and forcing models for the impredicative theory of classes
PY - 1980
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
KW - well-orderings; inductive constructions; axiomatization
UR - http://eudml.org/doc/268378
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.