Localizations of infinite subsets of omega
Abstract
In the present paper we are interested in properties of forcing notions which measure in a sense the distance between the ground model reals and the reals in the extension. We look at the ways the ``new'' reals can be aproximated by ``old'' reals. We consider localizations for infinite subsets of omega. Though each member of [omega]^omega can be identified with its increasing enumeration, the (standard) localizations of the enumeration does not provide satisfactory information on successive points of the set. They give us ``candidates'' for the n-th point of the set but the same candidates can appear several times for distinct n. That led to a suggestion that we should consider disjoint subsets of omega as sets of ``candidates'' for successive points of the localized set. We have two possibilities. Either we can demand that each set from the localization contains a limited number of members of the localized set or we can postulate that each intersection of that kind is large. Localizations of this kind are studied in section 1. In the second section we investigate localizations of infinite subsets of omega by sets of integers from the ground model. These localizations might be thought as localizations by partitions of omega into successive intervals.
Read the paper
Related studies
- eggNOG 5.0: a hierarchical, functionally and phylogenetically annotated orthology resource based on 5090 organisms and 2502 viruses
- Online Survival Analysis Software to Assess the Prognostic Value of Biomarkers Using Transcriptomic Data in Non-Small-Cell Lung Cancer
- OptiType: precision HLA typing from next-generation sequencing data
- Nicotinic Cholinergic System and COVID-19: In Silico Identification of an Interaction between SARS-CoV-2 and Nicotinic Receptors with Potential Therapeutic Targeting Implications
- Saccharomyces cerevisiae cells have three Omega class glutathione S-transferases acting as 1-Cys thiol transferases
- Hemolysis at low blood flow rates: in-vitro and in-silico evaluation of a centrifugal blood pump
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.