Generalized Galois-Tukey-connections between explicit relations on classical objects of real analysis. (English) Zbl 0829.03027
Judah, Haim (ed.), Set theory of the reals. Proceedings of a winter institute on set theory of the reals held at Bar-Ilan University, Ramat- Gan (Israel), January 1991. Providence, RI: American Mathematical Society (Distrib.), Isr. Math. Conf. Proc. 6, 619-643 (1993).
Summary: In this survey we are concerned with the study of structures and properties of classical real analysis as Lebesgue measure, Baire category, limit of sequences and absolute convergence of series, and we introduce a new (unified) treatment of phenomena which covers most of results in the field. To compare additivity of measure and category, D. H. Fremlin first used connections in this context. We generalize his approach to the study of connections between relations (inclusion, membership, existence of limit, absolute summability) restricted to classical objects of real analysis (ideals of null and meagre sets, reals, \(\ell^1\), \(\ell^\infty\) and \(\wp (\omega))\). We discuss also set-theoretic absoluteness of some connections in the context of properties of forcing extensions and aspects of the algebraic theory of categories.
For the entire collection see [Zbl 0821.00016].
For the entire collection see [Zbl 0821.00016].
MSC:
| 03E20 | Other classical set theory (including functions, relations, and set algebra) |
| 03E75 | Applications of set theory |
| 54A25 | Cardinality properties (cardinal functions and inequalities, discrete subsets) |
| 03E05 | Other combinatorial set theory |
| 40A05 | Convergence and divergence of series and sequences |
| 06A15 | Galois correspondences, closure operators (in relation to ordered sets) |
| 26A21 | Classification of real functions; Baire classification of sets and functions |
| 28A05 | Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets |
