caa a22 4500 388039728 CHVBK 20180307125017.0 cr unu---uuuuu 161130e199803 xx s 000 0 eng 10.2307/2586602 doi S0022481200015474 pii (NATIONALLICENCE)cambridge-10.2307/2586602 The algebraic sum of sets of real numbers with strong measure zero sets [Elektronische Daten] We prove the following theorems: (1) If X has strong measure zero and if Y has strong first category, then their algebraic sum has property S0. (2) If X has Hurewicz's covering property, then it has strong measure zero if, and only if, its algebraic sum with any first category set is a first category set. (3) If X has strong measure zero and Hurewicz's covering property then its algebraic sum with any set in is a set in . ( is included in the class of sets always of first category, and includes the class of strong first category sets.) These results extend: Fremlin and Miller's theorem that strong measure zero sets having Hurewicz's property have Rothberger's property, Galvin and Miller's theorem that the algebraic sum of a set with the γ-property and of a first category set is a first category set, and Bartoszyfński and Judah's characterization of -sets. They also characterize the property (*) introduced by Gerlits and Nagy in terms of older concepts. Copyright © Association for Symbolic Logic 1998 Nowik Andrej Ul. Kolobrzeska23/F8, Gdansk-Oliwa 80390, Poland, E-mail: andrzand@ghost.mimuw.edu.pl Scheepers Marion Department of Mathematics and Computer Science, Boise State University, Boise, Idaho 83725, USA, E-mail: marion@math.idbsu.edu Weiss Tomasz Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 301-324 0022-4812 63:1<301 1998 63 JSL https://doi.org/10.2307/2586602 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586602 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nowik Andrej Ul. Kolobrzeska23/F8, Gdansk-Oliwa 80390, Poland, E-mail: andrzand@ghost.mimuw.edu.pl NATIONALLICENCE 700 1- Scheepers Marion Department of Mathematics and Computer Science, Boise State University, Boise, Idaho 83725, USA, E-mail: marion@math.idbsu.edu NATIONALLICENCE 700 1- Weiss Tomasz Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 301-324 0022-4812 63:1<301 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge