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1. CMB 2006 (vol 49 pp. 11)

Bevelacqua, Anthony J.; Motley, Mark J.
 Going-Down Results for \$C_{i}\$-Fields We search for theorems that, given a \$C_i\$-field \$K\$ and a subfield \$k\$ of \$K\$, allow us to conclude that \$k\$ is a \$C_j\$-field for some \$j\$. We give appropriate theorems in the case \$K=k(t)\$ and \$K = k\llp t\rrp\$. We then consider the more difficult case where \$K/k\$ is an algebraic extension. Here we are able to prove some results, and make conjectures. We also point out the connection between these questions and Lang's conjecture on nonreal function fields over a real closed field. Keywords:\$C_i\$-fields, Lang's ConjectureCategories:12F, 14G

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