Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evasion and prediction --- the Specker phenomenon and Gross spaces   We study the set--theoretic combinatorics underlying the following two
algebraic phenomena.
  (1) A subgroup G leq Z^omega exhibits the Specker phenomenon iff every
homomorphism G to Z maps almost all unit vectors to 0. Let se be the size of
the smallest G leq Z^omega exhibiting the Specker phenomenon.
  (2) Given an uncountably dimensional vector space E equipped with a symmetric
bilinear form Phi over an at most countable field KK, (E,Phi) is strongly Gross
iff for all countably dimensional U leq E, we have dim(U^perp) leq omega.
  Blass showed that the Specker phenomenon is closely related to a
combinatorial phenomenon he called evading and predicting. We prove several
additional results (both theorems of ZFC and independence proofs) about evading
and predicting as well as se, and relate a Luzin--style property associated
with evading to the existence of strong Gross spaces.

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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci