Transfer theorems for topological structures

Fred Halpern

Vol. 61 (1975), No. 2, 427–440

DOI: 10.2140/pjm.1975.61.427

Abstract

Transfer theorems are obtained for the following mathematical situations.

𝒜 is a dense substructure of the compact structure X. {𝒜_i} is the set of all finitely generated substructures of X. F is a structure of functions from Y to the structure X.

The sentences transferred in the above situations are best described as “almost” positive, variables appearing in a negative subformula are quantified in a prescribed manner.

The main tools of this investigation are the manipulation of classical transfer theorems in the context of commutative diagrams, the ultraproduct construction, and the 𝒟-limit operation of Chang and Keisler’s “Continuous Model Theory.”

Mathematical Subject Classification

Primary: 02H05, 02H05

Milestones

Received: 20 December 1974

Published: 1 December 1975