CONTENTSIntroduction......................... 5Section I. Preliminaries............ 6 § 1. Notation..................... 6 § 2. Ackermann’s set theory and some extensions................. 7 § 3. Absoluteness............................................... 8 § 4. Ordinals................................................... 9 § 5. Reflection principles...................................... 10Section 2. The usual notion of constructibility.............. 11 § 1. General considerations about the constructibility in A...... 11 § 2. Definitions of some syntactic and semantic notions.......... 12 § 3. The formula ...................................... 15 § 4. Satisfaction................................................. 16 § 5. Extendability of ZF-models to models of A.................... 17Section 3. The constructible universe Λ........................... 19 § 1. The formula H(w, β, V)...................................... 19 § 2. Some results concerning the formula ............... 20 § 3. Proof of the main theorem.................................... 24 § 4. The minimal model of A...................................... 28 § 5. Ordinal definable classes................................... 29 § 6. Constructibility in related theories........................ 33References....................................................... 36
@book{bwmeta1.element.zamlynska-08b8a6a5-86e6-4808-b7f7-6a8ea3cd9c39,
author = {C. Alkor},
title = {Constructibility in Ackermann's set theory},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1982},
zbl = {0519.03040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-08b8a6a5-86e6-4808-b7f7-6a8ea3cd9c39}
}
C. Alkor. Constructibility in Ackermann's set theory. GDML_Books (1982), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-08b8a6a5-86e6-4808-b7f7-6a8ea3cd9c39/