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Constructibility in Ackermann's set theory

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Alkor C.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction......................... 5 Section I. Preliminaries............ 6 § 1. Notation..................... 6 § 2. Ackermann's set theory and some extensions................. 7 § 3. Absoluteness............................................... 8 § 4. Ordinals................................................... 9 § 5. Reflection principles...................................... 10 Section 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 $w=\^{L}_β$...................................... 15 § 4. Satisfaction................................................. 16 § 5. Extendability of ZF-models to models of A.................... 17 Section 3. The constructible universe Λ........................... 19 § 1. The formula H(w, β, V)...................................... 19 § 2. Some results concerning the formula $w = H_β$............... 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........................ 33 References....................................................... 36

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1 Alkor C.

1 1982

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Constructibility in Ackermann's set theory