Some Results in Stationary Logic

a-determinate A₁ analogue apply argument assume atomic axioms back-and-forth system Barwise Chapter claim clearly closed completeness condition consider consistent construct COROLLARY countable criterion define definition denote desired determinate direct products disjoint sums easy elementary elements equivalence example exist extension ɛ F fact families Finally finite first-order formula function give given Hence holds indexed interpolation K(aa L-structures L(aa language Lemma limit Low aa Math nice notion obtain ordinal parameters pick preserved probability proof properties Proposition prove putting quantifier rank relation Remark respectively rn f satisfy second-order sentence sequence similar standard stat stat t₁ stationary logic strongly omits structures subsets suffices Suppose symbol t₂ Theorem theory thesis tree true University usual variables verify w₁ weak model write