A saturation property of structures obtained by forcing with a compact family of random variables
arXiv:1207.1548 · doi:10.1007/s00153-012-0304-9
Abstract
A method how to construct Boolean-valued models of some fragments of arithmetic was developed in Krajicek (2011), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random variables defined on a pseudo-finite sample space. We show that under a fairly natural condition on the family (called compactness in K.(2011)) the resulting structure has a property that is naturally interpreted as saturation for existential types. We also give an example showing that this cannot be extended to universal types.
arXiv commentpreprint February 2012