Generic expansions of structures

Publisher: Cambridge University Press

E-ISSN: 1943-5886|38|4|561-570

ISSN: 0022-4812

Source: The Journal of Symbolic Logic, Vol.38, Iss.4, 1973-12, pp. : 561-570

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

In this paper, Cohen's forcing technique is applied to some problems in model theory. Forcing has been used as a model-theoretic technique by several people, in particular, by A. Robinson in a series of papers [1], [10], [11]. Here forcing will be used to expand a family of structures in such a way that weak second-order embeddings are preserved. The forcing situation resembles that in Solovay's proof that for any theorem φ of GB (Godel-Bernays set theory with a strong form of the axiom of choice), if φ does not mention classes, then it is already a theorem of ZFC. (See [3, p. 105] and [2, p. 77].)