This article is cited in 1 paper

The transcendental rank of the formulas of an $\aleph_1$-categorical theory

B. I. Zil'ber

Novosibirsk State University

Abstract: In this paper we investigate the transcendental rank introduced by Morley. We introduce the concept of a fibering and prove a series of lemmas about fibering, on the basis of which we prove the main theorems: on an estimate for the rank of a formula (Theorem 3); on the summation of ranks (Theorem 2); and a reproof of Baldwin's theorem on the finiteness of the rank of $\aleph_1$-categorical theories (Theorem 1).

UDC: 51.01

Received: 08.08.1972

 English version: Mathematical Notes, 1974, 15:2, 182–186

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