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Journal of the London Mathematical Society 1996 53(1):19-27; doi:10.1112/jlms/53.1.19
© 1996 by London Mathematical Society
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© The London Mathematical Society

Evasion and Prediction II

Jörg Brendle and Saharon Shelah

Mathematisches Institut der Universität Auf der Morgenstelle 10, 72076 Tübingen, Germany
Department of Mathematics, Hebrew University Givat Ram, 91904 Jerusalem, Israel and Department of Mathematics, Rutgers University New Brunswick, NJ 08854, USA

Received 24 June 1994.

A subgroup G ≤ Z{omega} exhibits the Specker phenomenon if every homomorphism G -> Z maps almost all unit vectors to 0. We give several combinatorial characterizations of the cardinal se, the size of the smallest G ≤ Z{omega} exhibiting the Specker phenomenon. We also prove the consistency of b > e, where b is the unbounding number and e the evasion number. Our results answer several questions addressed by Blass.

Current address: Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA

First author supported by DFG grant Br 1420/1-1. Second author supported by the Edmund Landau Center for research in Mathematical Analysis (sponsored by the MINERVA-foundation, Germany).


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