A new combinatorial characterization of the minimal cardinality of a subset of R which is not of first category
| dc.creator | Tyszka, Apoloniusz | |
| dc.date | 1999-11-17 | |
| dc.date | 1999-11-30 | |
| dc.date.accessioned | 2026-07-07T05:31:38Z | |
| dc.date.available | 2026-07-07T05:31:38Z | |
| dc.description | Let M denote the ideal of first category subsets of R. We prove that min{card X: X \subseteq R, X \not\in M} is the smallest cardinality of a family S \subseteq {0,1}^ωwith the property that for each f: ω-> \bigcup_{n \in ω}{0,1}^n there exists a sequence {a_n}_{n \in ω} belonging to S such that for infinitely many i \in ωthe infinite sequence {a_{i+n}}_{n \in ω} extends the finite sequence f(i). We inform that S \subseteq {0,1}^ωis not of first category if and only if for each f: ω-> \bigcup_{n \in ω}{0,1}^n there exists a sequence {a_n}_{n \in ω} belonging to S such that for infinitely many i \in ωthe infinite sequence {a_{i+n}}_{n \in ω} extends the finite sequence f(i). | |
| dc.description | 4 pages, LaTeX 209, a new theorem added (see Abstract and Note on p.2) | |
| dc.identifier | https://arxiv.org/abs/math/9911122 | |
| dc.identifier | http://arxiv.org/abs/math/9911122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79420 | |
| dc.subject | Logic | |
| dc.subject | 03E05 (Primary) 54A25 (Primary) 26A03 (Secondary) | |
| dc.title | A new combinatorial characterization of the minimal cardinality of a subset of R which is not of first category | |
| dc.type | text |