Lattices of Intermediate Theories via Ruitenburg's Theorem

证明论中的稀释器与中间点类

Proof-theoretic dilator and intermediate pointclasses

本文研究了证明论中稀释器与中间点类之间的系统性联系，揭示了Σ^1_2证明论在连接这两种一般化标准序数分析中的关键作用。

Epsilon Theorems in Intermediate Logics

Any intermediate propositional logic (i.e., a logic including intuitionistic logic and contained in classical logic) can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert's $\varepsilon$-calculus. The first and second $\varepsilon$-theorems for classical logic establish conservativity of the $\varepsilon$-calculus over its classical base logic. It is well known that the second $\varepsilon$-theorem fails for the intuitionistic $\varepsilon$-calculus, as prenexation is impossible. The paper investigates the effect of ad…

Structural completeness in propositional logics of dependence

In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of substitutions under which the logics are closed. We obtain an analogues result with respect to stable substitutions, for the negative variants of some well-known intermediate logics, which are intermediate theories that are closely related to inquisitive logic.