## Bounds on Transfer Principles for Algebraically Closed and Complete Discretely Valued Fields, Issue 204 |

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algebraic set algebraically closed fields Artin conjecture Assume the hypotheses atm(B atomic formula B(xj to xn bnd(i coefficients of f common root complete valued field convergence COR(G decision procedure defined definition of e(P deg(F DFN.b equivalence classes equivalence relation exists f and h field of characteristic figure finite set graph h/gcd(h Hensel's lemma holds hyperplanes implies INC(F INC(G independent w. r. t. induction integers irreducible component leading coefficient monic multiplicities Newton polygon nonzero number of variables ord(f p-adic p-adic valuation poly(B polygon of F polynomials pro(E proj(P PROOF proves Qj xj Qn xn quantifier-free formula radius of convergence rational numbers RC(f RD(f real numbers remat f residue class field resp(f roots of F set of representatives shows single root size(f slope statement subcase subset terms(B theorem theory of algebraically trailing coefficient transfer principles valuation xj to xn