Strong logics of first and second order

摘要: In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation logic the co-logic /?-logic, isolating two facets absoluteness, namely, generic invariance faithfulness. It turns out is relative in sense stronger background assumptions secure greater degrees absoluteness. Our aim to hierarchies are generically invariant faithful against backdrop strongest large cardinal hypotheses. show there a close correspondence between characterize each hierarchy. On first-order side, leads new presentation Woodin's Q-logic. second-order compare full argue comparison lends support Quine's claim really set theory sheep's clothing. This concerned order. At most abstract level, has following general form: Let L be language let (x) formula defines class L-structures. Then, for recursively enumerable T sentences L, sentence ip